# 1403 Multiplication Table Challenge

Just because you’re not in elementary school anymore doesn’t mean that the multiplication table can’t be a challenge. This one certainly is. Can you write the numbers 1 to 10 in the four factor areas so that this multiplication table works with the given clues? Don’t get discouraged; it will probably take you at least 15 minutes just to put those factors in the right places. Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll share some information about the puzzle number, 1403:

• 1403 is a composite number.
• Prime factorization: 1403 = 23 × 61
• 1403 has no exponents greater than 1 in its prime factorization, so √1403 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 1403 has exactly 4 factors.
• The factors of 1403 are outlined with their factor pair partners in the graphic below. 1403 is the hypotenuse of a Pythagorean triple:
253-1380-1403 which is 23 times (11-60-61)

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# 1402 Mystery Level

Mystery level puzzles may be very difficult or relatively easy. How much trouble will this one be? You’ll have to try it to see! Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll tell you a little bit about the number 1402:

• 1402 is a composite number.
• Prime factorization: 1402 = 2 × 701
• 1402 has no exponents greater than 1 in its prime factorization, so √1402 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 1402 has exactly 4 factors.
• The factors of 1402 are outlined with their factor pair partners in the graphic below. 1402 is the hypotenuse of a Pythagorean triple:
31² + 21² = 1402

1402 is the hypotenuse of a Pythagorean triple:
520-1302-1402 which is 2 times (260-651-701)
and can also be calculated from 2(31)(21), 31² – 21², 31² + 21²

# 1401 Roasting Over an Open Fire

I went camping last week. My family roasted hotdogs. Some people refer to them as mystery meat. Others roasted marshmallows. I was surprised to learn that almost all brands of marshmallows have blue dye in them.  I’m told that without that blue dye the marshmallows will lose their whiteness as they sit on store shelves. Why they have to be that white is a mystery to me.

Here’s a mystery level puzzle for you to solve. It looks a lot like the utensil that was used to roast the hotdogs and marshmallows. Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll tell you something about the number 1401:

• 1401 is a composite number.
• Prime factorization: 1401 = 3 × 467
• 1401 has no exponents greater than 1 in its prime factorization, so √1401 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 1401 has exactly 4 factors.
• The factors of 1401 are outlined with their factor pair partners in the graphic below. 1401 is the difference of two squares in two different ways. Can you figure out what those ways are?

# 1399 and Level 6

The eligible common factors of 48 and 72 are 6, 8, and 12. The common factors for 10 and 30 are 5 and 10.  Don’t guess and check the possibilities! Can you figure out the logic needed to start this puzzle? Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Here’s a little information about the number 1399:

• 1399 is a prime number.
• Prime factorization: 1399 is prime.
• 1399 has no exponents greater than 1 in its prime factorization, so √1399 cannot be simplified.
• The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1399 has exactly 2 factors.
• The factors of 1399 are outlined with their factor pair partners in the graphic below. How do we know that 1399 is a prime number? If 1399 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1399. Since 1399 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, or 37, we know that 1399 is a prime number.

1399 is the difference of two squares:
700² – 699² = 1399

# 1398 and Level 5

You might find this puzzle to be a little tricky, but if you always use logic before you write any of the factors, you should succeed! Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Here is some information about the number 1398:

• 1398 is a composite number.
• Prime factorization: 1398 = 2 × 3 × 233
• 1398 has no exponents greater than 1 in its prime factorization, so √1398 cannot be simplified.
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1398 has exactly 8 factors.
• The factors of 1398 are outlined with their factor pair partners in the graphic below. 1398 is the hypotenuse of a Pythagorean triple:
630-1248-1398 which is 6 times (105-208-233)

# 1397 and Level 4

I bet you know enough multiplication facts to get this puzzle started. Once you’ve started it, you might as well finish it. You will feel so clever when you do! Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll write a little bit about the puzzle number, 1397:

• 1397 is a composite number.
• Prime factorization: 1397 = 11 × 127
• 1397 has no exponents greater than 1 in its prime factorization, so √1397 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 1397 has exactly 4 factors.
• The factors of 1397 are outlined with their factor pair partners in the graphic below. 1397 is the difference of two squares two different ways:
699² – 698² = 1397
69² – 58² = 1397

# 1394 and Level 2

The factors and most of the products are missing from this multiplication table, and the ones that are there aren’t in there usual places. Can you figure out where everything goes? Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Now I’ll write a little bit about the puzzle number, 1394:

• 1394 is a composite number.
• Prime factorization: 1394 = 2 × 17 × 41
• 1394 has no exponents greater than 1 in its prime factorization, so √1394 cannot be simplified.
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1394 has exactly 8 factors.
• The factors of 1394 are outlined with their factor pair partners in the graphic below. 1394 is the hypotenuse of FOUR Pythagorean triples:
306-1360-1394 which is (9-40-41) times 34
370-1344-1394 which is 2 times (185-672-697)
656-1230-1394 which is (8-15-17) times 82
910-1056-1394 which is 2 times (455-528-697)

# 1391 and Level 1

Many of the clues in this puzzle have double digits. If you know why they do, then you can find all the factors and solve this puzzle! Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Here’s some information about the number 1391:

• 1391 is a composite number.
• Prime factorization: 1391 = 13 × 107
• 1391 has no exponents greater than 1 in its prime factorization, so √1391 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 1391 has exactly 4 factors.
• The factors of 1391 are outlined with their factor pair partners in the graphic below. 1391 is the hypotenuse of a Pythagorean triple:
535-1284-1391 which is (5-12-13) times 107

# 1389 Positive Trinomial Puzzle

Today on Twitter, Mr. Allen requested some good problem-solving resources for quadratics. He made up one himself.

I decided to make one as well. It is similar to my other Find the Factors puzzles. You will have to use logic to solve it, but in many ways, it will be easier to solve than most of my regular puzzles. Like always, there is only one solution. Print the puzzles or type the solution in this excel file: 12 Factors 1389-1403

Every term is positive so if you already know how to factor trinomials it should be relatively easy to solve. All the factors from (x + 1) to (x + 9) need to appear exactly one time in both the first column and the top row of the puzzle.  Once all the factors are found, the puzzle is solved, but you can find all the products of those factors and write them in the body of the puzzle if you want.

Since this is my 1389th post, here’s a little bit about that number:

• 1389 is a composite number.
• Prime factorization: 1389 = 3 × 463
• 1389 has no exponents greater than 1 in its prime factorization, so √1389 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 1389 has exactly 4 factors.
• The factors of 1389 are outlined with their factor pair partners in the graphic below. 1389 is the difference of two squares in two different ways:
695² – 694² = 1389
233² – 230² = 1389

# 1388 Mystery Level

Sometimes puzzles start out easy enough but get a little more complicated later on. Does that happen with this puzzle? There’s only one way to find out! Print the puzzles or type the solution in this excel file: 10 Factors 1373-1388

Here are some facts about the number 1388:

• 1388 is a composite number.
• Prime factorization: 1388 = 2 × 2 × 347, which can be written 1388 = 2² × 347
• 1388 has at least one exponent greater than 1 in its prime factorization so √1388 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1388 = (√4)(√347) = 2√347
• The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1388 has exactly 6 factors.
• The factors of 1388 are outlined with their factor pair partners in the graphic below. 1388 is the difference of two squares:
348² – 346² = 1388