Occasionally, we hear that the number of Easter eggs that are found is one or two less than the number of eggs that were hidden. Still most of the time, all the eggs and candies do get found. You really have no trouble finding all those goodies, and the Easter Egg Hunt seems like it is over in seconds. You can find Easter Eggs but can you find factors? Here’s an **Easter Basket** Find the Factors 1 – 10 Challenge Puzzle for you. I guarantee it won’t be done in seconds. Can you find all the factors? I dare you to try!

# Find the Factors Challenge

# 1350 Logic is at the Heart of This Puzzle

By simply changing two clues of that recently published puzzle that I rejected, I was able to create a love-ly puzzle that can be solved entirely by logic. Can you figure out where to put the numbers from 1 to 12 in each of the four outlined areas that divide the puzzle into four equal sections? If you can, my heart might just skip a beat!

If you need some tips on how to get started on this puzzle, check out this video:

Now I’ll tell you a few things about the number 1350:

- 1350 is a composite number.
- Prime factorization: 1350 = 2 × 3 × 3 × 3 × 5 × 5, which can be written 1350 = 2 × 3³ × 5²
- The exponents in the prime factorization are 1, 3 and 2. Adding one to each and multiplying we get (1 + 1)(3 + 1)(2 + 1) = 2 × 4 × 3 = 24. Therefore 1350 has exactly 24 factors.
- Factors of 1350: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350
- Factor pairs: 1350 = 1 × 1350, 2 × 675, 3 × 450, 5 × 270, 6 × 225, 9 × 150, 10 × 135, 15 × 90, 18 × 75, 25 × 54, 27 × 50 or 30 × 45
- Taking the factor pair with the largest square number factor, we get √1350 = (√225)(√6) = 15√6 ≈ 36.74235

1350 is the sum of consecutive prime numbers two ways:

It is the sum of the fourteen prime numbers from 67 to 131, and

673 + 677 = 1350

1350 is the hypotenuse of two Pythagorean triples:

810-1080-1350 which is (3-4-**5**) times **270**

378-1296-1350 which is (7-24-**25**) times **54**

1350 is also the **20**th nonagonal number because **20**(7 · **20** – 5)/2 = 1350

# 1349 A Rejected Puzzle

I was in the mood to make a Find the Factors Challenge Puzzle that used the numbers from 1 to 12 as the factors. I’ve never made such a large puzzle before, but after I made it, I rejected it. All the puzzles I make must meet certain standards: they must have a unique solution, and that solution must be obtainable by using logic. Although the “puzzle” below has a unique solution, and you can fill in a few of the cells using logic, you would have to use guess and check to finish it. Besides that, you wouldn’t be able to know if you guessed right until almost the entire puzzle was completed. Thus, it doesn’t meet my standards.

Even though the puzzle was rejected, there were still some things about it that I really liked. In my next post, I’ll publish a slightly different puzzle that uses some of the same necessary logic that I appreciated but doesn’t rely on guess and check at all. This is NOT the first time I have tweaked a puzzle that didn’t initially meet my standards to make it acceptable. I just thought I would share the process this time. If you try to solve it, you will be able to see the problem with the puzzle yourself.

Now I’ll share some information about the number 1349:

- 1349 is a composite number.
- Prime factorization: 1349 = 19 × 71
- 1349 has no exponents greater than 1 in its prime factorization, so √1349 cannot be simplified.
- The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1349 has exactly 4 factors.
- The factors of 1349 are outlined with their factor pair partners in the graphic below.

1349 is the sum of 13 consecutive primes, and it is also the sum of three consecutive primes:

73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 = 1349

443 + 449 + 457 = 1349

# 1319 Challenge Puzzle

There are nineteen clues in this challenge puzzle, including two 50’s, two 20’s, two 8’s, and two 12’s. Some of those duplicates might make it more difficult for you to find the one and only solution to the puzzle. I’m very curious about how you do with it!

Print the puzzles or type the solution in this excel file: 12 factors 1311-1319

Now I’ll share some facts about the number 1319:

- 1319 is a prime number.
- Prime factorization: 1319 is prime.
- The exponent of prime number 1319 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1319 has exactly 2 factors.
- Factors of 1319: 1, 1319
- Factor pairs: 1319 = 1 × 1319
- 1319 has no square factors that allow its square root to be simplified. √1319 ≈ 36.31804

**How do we know that ****1319**** is a prime number?** If 1319 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1319 ≈ 36.3. Since 1319 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1319 is a prime number.

# 1220 Challenge Puzzle

The last challenge puzzle was particularly difficult. This one won’t be nearly as bad. Try it and see if you can figure it out!

Print the puzzles or type the solution in this excel file: 12 factors 1211-1220

Here are a few facts about the number 1220:

- 1220 is a composite number.
- Prime factorization: 1220 = 2 × 2 × 5 × 61, which can be written 1220 = 2² × 5 × 61
- The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1220 has exactly 12 factors.
- Factors of 1220: 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220
- Factor pairs: 1220 = 1 × 1220, 2 × 610, 4 × 305, 5 × 244, 10 × 122, or 20 × 61
- Taking the factor pair with the largest square number factor, we get √1220 = (√4)(√305) = 2√305 ≈ 34.9285

1220 is the sum of consecutive prime numbers: 607 + 613 = 1220

1220 is the sum of two squares two different ways:

32² + 14² = 1220

34² + 8² = 1220

1220 is the hypotenuse of four Pythagorean triples:

220-1200-1220 which is **20** times (11-60-**61**)

544-1092-1220 calculated from 2(34)( 8), 34² – 8², 34² + 8²

and is also **4** times (136-273-**305**)

828-896-1220 calculated from 32² – 14², 2(32)(14), 32² + 14²

and is also 4 times (207-224-**305**)

732-976-1220 which is (3-4-**5**) times **244**

# 1210 Challenge Puzzle

Some of these Find the Factors Challenge puzzles are easier than others. This one is probably not one of the easier ones. Have fun with it anyway!

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Now I’ll share a few facts about the number 1210:

- 1210 is a composite number.
- Prime factorization: 1210 = 2 × 5 × 11 × 11, which can be written 1210 = 2 × 5 × 11²
- The exponents in the prime factorization are 1, 2, and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1210 has exactly 12 factors.
- Factors of 1210: 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210
- Factor pairs: 1210 = 1 × 1210, 2 × 605, 5 × 242, 10 × 121, 11 × 110, or 22 × 55,
- Taking the factor pair with the largest square number factor, we get √1210 = (√121)(√10) = 11√10 ≈ 34.78505

1210 is the hypotenuse of a Pythagorean triple:

726-968-1210 which is (3-4-5) times 242

1210 is

1122211 in BASE 3

626 in BASE 14

181 in BASE 31

# 1198 Challenge Puzzle

You can solve this Find the Factors 1 – 10 puzzle if you use logic. Guessing and checking will likely only frustrate you. Go ahead and give logic a try!

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Now I’ll share some facts about the number 1198:

- 1198 is a composite number.
- Prime factorization: 1198 = 2 × 599
- The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1198 has exactly 4 factors.
- Factors of 1198: 1, 2, 599, 1198
- Factor pairs: 1198 = 1 × 1198 or 2 × 599
- 1198 has no square factors that allow its square root to be simplified. √1198 ≈ 34.61214

1198 is also palindrome 262 in BASE 23

# 1186 Challenge Puzzle

It shouldn’t be too hard to make your first move in this puzzle. After that, I don’t make any guarantees. You just need to write each number from 1 to 10 in each of the four boldly outlined areas so that the given clues are the products of the factors you wrote. Use logic to find all the factors and have fun doing it!

Print the puzzles or type the solution in this excel file: 10-factors-1174-1186

What have I found out about the number 1186?

- 1186 is a composite number.
- Prime factorization: 1186 = 2 × 593
- The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1186 has exactly 4 factors.
- Factors of 1186: 1, 2, 593, 1186
- Factor pairs: 1186 = 1 × 1186 or 2 × 593
- 1186 has no square factors that allow its square root to be simplified. √1186 ≈ 34.43835

31² + 15² = 1186

1186 is the hypotenuse of a Pythagorean triple:

736-930-1186 calculated from 31² – 15², 2(31)(15), 31² + 15²

1186 is palindrome 989 in BASE 11

# 1173 Challenge Puzzle

Getting started on this Challenge Puzzle will take some thinking, but solving it is worth all the effort. Remember use logic, not guess and check, and you will eventually be successful!

Print the puzzles or type the solution in this excel file: 12 factors 1161-1173

Here’s some information about the number 1173:

- 1173 is a composite number.
- Prime factorization: 1173 = 3 × 17 × 23
- The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1173 has exactly 8 factors.
- Factors of 1173: 1, 3, 17, 23, 51, 69, 391, 1173
- Factor pairs: 1173 = 1 × 1173, 3 × 391, 17 × 69, or 23 × 51
- 1173 has no square factors that allow its square root to be simplified. √1173 ≈ 34.24909

1173 is the hypotenuse of a Pythagorean triple:

552-1035-1173 which is (8-15-**17**) times **69**

1173 is palindrome 3B3 in BASE 18 (B is 11 base 10)

because 3(18²) + 11(18) + 3(1) = 1173

# 1160 Find the Factors Challenge

I love this particular puzzle. I had so much fun figuring out the logic. It’s a little bit complicated, but once you figure out the first move, it shouldn’t take too long to figure out most of the rest of the puzzle. Do give it a try!

Print the puzzles or type the solution in this excel file: 10-factors-1148-1160

Here are some facts about the number 1160:

- 1160 is a composite number.
- Prime factorization: 1160 = 2 × 2 × 2 × 5 × 29, which can be written 1160 = 2³ × 5 × 29
- The exponents in the prime factorization are 3, 1, and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1)(1 + 1) = 4 × 2 × 2 = 16. Therefore 1160 has exactly 16 factors.
- Factors of 1160: 1, 2, 4, 5, 8, 10, 20, 29, 40, 58, 116, 145, 232, 290, 580, 1160
- Factor pairs: 1160 = 1 × 1160, 2 × 580, 4 × 290, 5 × 232, 8 × 145, 10 × 116, 20 × 58, or 29 × 40
- Taking the factor pair with the largest square number factor, we get √1160 = (√4)(√290) = 2√290 ≈ 34.05877

26² + 22² = 1160

34² + 2² = 1160

1160 is the hypotenuse of FOUR Pythagorean triples:

136-1152-1160 which is **8** times (17-144-**145**)

(It can also be calculated from 2(34)(2), 34² – 2², 34² + 2²)

192-1144-1160 which is **8** times (24-143-**145**)

(It can also be calculated from 26² – 22², 2(26)(22), 26² + 22²)

696-928-1160 which is (3-4-**5**) times **232**

800-840-1160 which is (20-21-**29**) times **40**

1160 is a palindrome when it is written in these three bases:

It’s 808 in BASE 12 because 8(12²) + 8(1) = 8(145) = 1160,

525 in BASE 15 because 5(15²) + 2(15) + 5(1) = 1160, and

404 in BASE 17 because 4(17²) + 4(1) = 4(290) = 1160