Today’s puzzle looks like a giant times table with a big X in the middle. The factors for this times table are not in the usual places. Can you figure out where they all go?

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

Here are a few facts about the number 1204:

• 1204 is a composite number.
• Prime factorization: 1204 = 2 × 2 × 7 × 43, which can be written 1204 = 2² × 7 × 43
• 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 1204 has exactly 12 factors.
• Factors of 1204: 1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602, 1204
• Factor pairs: 1204 = 1 × 1204, 2 × 602, 4 × 301, 7 × 172, 14 × 86, or 28 × 43
• Taking the factor pair with the largest square number factor, we get √1204 = (√4)(√301) = 2√301 ≈ 34.6987

1204 is the difference of two squares two different ways:
302² – 300² = 1204
50² – 36² = 1204

At the top of this level 3 puzzle are two clues that will tell you where to put three of the factors needed to solve the puzzle. After you find those three clues work down looking at the clues cell by cell until you have the entire puzzle solved.

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

Here are a few facts about the number 1203:

• 1203 is a composite number.
• Prime factorization: 1203 = 3 × 401
• 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 1203 has exactly 4 factors.
• Factors of 1203: 1, 3, 401, 1203
• Factor pairs: 1203 = 1 × 1203 or 3 × 401
• 1203 has no square factors that allow its square root to be simplified. √1203 ≈ 34.68429

Since 1203 is only made from three consecutive numbers (1, 2, 3) and zeros, it has to be divisible by 3.

1203 is the hypotenuse of a Pythagorean triple:
120-1197-1203 which is 3(40-399-401)

I am certain that you can fill in the numbers 1 to 10 one time in both the top row and the first column so that this puzzle can become a multiplication table. All you have to do is give it an honest try.

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

Now I’ll write a few things about the number 1202:

• 1202 is a composite number.
• Prime factorization: 1202 = 2 × 601
• 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 1202 has exactly 4 factors.
• Factors of 1202: 1, 2, 601, 1202
• Factor pairs: 1202 = 1 × 1202 or 2 × 601
• 1202 has no square factors that allow its square root to be simplified. √1202 ≈ 34.66987

29² + 19² = 1202

1202 is the hypotenuse of a Pythagorean triple:
480-1102-1202 calculated from 29² – 19², 2(29)(19), 29² + 19²

2(24² + 5²) = 2(601) = 1202 so that Pythagorean triple can also be calculated from
2(2)(24)(5), 2(24² – 5²), 2(24² + 5²)

Try out both ways to get the triple!

In this puzzle, the permissible common factors of 48 and 72 are 6, 8, and 12. For clues 8 and 16, you can choose from common factors 2, 4, or 8. Which choices will make the puzzle work? I’m not telling, but I promise that the entire puzzle can be solved using logic and a basic knowledge of a 12×12 multiplication table. There is only one solution.

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

Here are some facts about the number 1196:

• 1196 is a composite number.
• Prime factorization: 1196 = 2 × 2 × 13 × 23, which can be written 1196 = 2² × 13 × 23
• 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 1196 has exactly 12 factors.
• Factors of 1196: 1, 2, 4, 13, 23, 26, 46, 52, 92, 299, 598, 1196
• Factor pairs: 1196 = 1 × 1196, 2 × 598, 4 × 299, 13 × 92, 23 × 52, or 26 × 46
• Taking the factor pair with the largest square number factor, we get √1196 = (√4)(√299) = 2√299 ≈ 34.58323

1196 is the hypotenuse of a Pythagorean triple:
460-1104-1196 which is (5-12-13) times 92

1196 is a palindrome in three different bases:
It’s 14241 in BASE 5,
838 in BASE 12, and
616 in BASE 14

The new school year is underway. Much may have been forgotten over the summer. If you don’t quite remember all the multiplication tables, this puzzle book can help you remember them AND help your brain grow. You might still find it a challenge, but that only makes it more fun!

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

Now I’ll share a few facts about the number 1195:

• 1195 is a composite number.
• Prime factorization: 1195 = 5 × 239
• 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 1195 has exactly 4 factors.
• Factors of 1195: 1, 5, 239, 1195
• Factor pairs: 1195 = 1 × 1195 or 5 × 239
• 1195 has no square factors that allow its square root to be simplified. √1195 ≈ 34.56877

1195 is also the hypotenuse of a Pythagorean triple:
717-956-1195 which is (3-4-5) times 239

The more multiplication facts you know, the easier these puzzles become. Working on these puzzles can help you learn the multiplication table better. Go ahead,  give this puzzle a try!

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

Here are a few facts about the number 1194:

• 1194 is a composite number.
• Prime factorization: 1194 = 2 × 3 × 199
• 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 1194 has exactly 8 factors.
• Factors of 1194: 1, 2, 3, 6, 199, 398, 597, 1194
• Factor pairs: 1194 = 1 × 1194, 2 × 597, 3 × 398, or 6 × 199
• 1194 has no square factors that allow its square root to be simplified. √1194 ≈ 34.5543

1194 is the sum of consecutive prime numbers two ways:
131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 = 1194
283 + 293 + 307 + 311 = 1194

1194 is palindrome 424 in BASE 17

The common factors of 108 and 120 are 1, 2, 3, 4, 6, and 12, but pick the one that will only put numbers from 1 to 12 in the first column. Then work down that first column cell by cell writing in the factors of the clues as you go. Each number from 1 to 12 must go somewhere in both the first column and the top row.

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

Now I’ll share some information about the number 1190:

• 1190 is a composite number.
• Prime factorization: 1190 = 2 × 5 × 7 × 17
• The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 110. Therefore 1190 has exactly 110 factors.
• Factors of 1190: 1, 2, 5, 7, 10, 14, 17, 34, 35, 70, 85, 119, 170, 238, 595, 1190
• Factor pairs: 1190 = 1 × 1190, 2 × 595, 5 × 238, 7 × 170, 10 × 119, 14 × 85, 17 × 70, or 34 × 35
• 1190 has no square factors that allow its square root to be simplified. √1190 ≈ 34.49638

Because 1190 is the product of consecutive numbers 34 and 35, we know it is the sum of the first 34 EVEN numbers. Instead of writing all of those 34 numbers, we can use a some mathematical shorthand and simply write:
2 + 4 + 6 + 8 + . . . + 64 + 66 + 68 = 1190

1190 is the hypotenuse of FOUR Pythagorean triples:
182-1176-1190 which is 14 times (13-84-85)
504-1078-1190 which is 14 times (36-77-85)
560-1050-1190 which is (8-15-17) times 70
714-952-1190 which is (3-4-5) times 238

I like the way 1190 looks in some other bases:
It’s 707 in BASE 13 because 7(13²) + 7(1) = 7(169 + 1) = 7(170) = 1190,
545 in BASE 15,
2A2 in BASE 22,
1C1 in BASE 29 (C is 12 base 10),
and Y0 in BASE 35 (Y is 34 base 10) because 34(35) = 1190