If you know how to multiply and divide, then you can solve this puzzle. Just use logic to find the factors from 1 to 12 that go in the first column and the top row. Go ahead give it a try!

Print the puzzles or type the solution in this excel file: 12 factors 942-950

Now here’s a little about the number 947:

947 is a prime number that can be written as the sum of seven consecutive prime numbers:
113 + 127 + 131 + 137 + 139 + 149 + 151 = 947

947 is a palindrome in three other bases:
3B3 BASE 16 (B is 11 base 10), because 3(16²) + 11(16¹) + 3(16⁰) = 947
232 BASE 21 because 2(21²) + 3(21¹) + 2(21⁰) = 947
1L1 BASE 22 (L is 21 BASE 10), because 1(22²) + 21(22¹) + 1(22⁰) = 947

• 947 is a prime number.
• Prime factorization: 947 is prime.
• The exponent of prime number 947 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 947 has exactly 2 factors.
• Factors of 947: 1, 947
• Factor pairs: 947 = 1 × 947
• 947 has no square factors that allow its square root to be simplified. √947 ≈ 30.773365

How do we know that 947 is a prime number? If 947 were not a prime number, then it would be divisible by at least one prime number less than or equal to √947 ≈ 30.8. Since 947 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, or 29, we know that 947 is a prime number.

The division facts needed to solve today’s puzzle are not complicated. You can fill in all the cells of this puzzle if you know the multiplication facts from 1 × 1 to 12 × 12.

Print the puzzles or type the solution in this excel file: 12 factors 942-950

Now here are some facts about the number 944:

944 is divisible by 2 because it is even.
944 is divisible by 4 because the last number is divisible by 4 and the digit before it is even.
944 can be evenly divided by 8 because 44 is divisible by 4, but not by 8, and the digit before 44 is odd.

944 is a funny-looking palindrome, 1I1, in BASE 23 (I is 18 in base 10) because 1(23²) + 18(23¹) + 1(23⁰) = 944

• 944 is a composite number.
• Prime factorization: 944 = 2 × 2 × 2 × 2 × 59, which can be written 944 = 2⁴ × 59
• The exponents in the prime factorization are 4 and 1. Adding one to each and multiplying we get (4 + 1)(1 + 1) = 5 × 2 = 10. Therefore 944 has exactly 10 factors.
• Factors of 944: 1, 2, 4, 8, 16, 59, 118, 236, 472, 944
• Factor pairs: 944 = 1 × 944, 2 × 472, 4 × 236, 8 × 118, or 16 × 59
• Taking the factor pair with the largest square number factor, we get √944 = (√16)(√59) = 4√59 ≈ 30.72458

Level 2 puzzles aren’t very tricky, but maybe this one is a little bit. Can you write the factors from 1 to 12 in both the first column and the top row so that this puzzle functions as a multiplication table?

Print the puzzles or type the solution in this excel file: 12 factors 942-950

Now I’ll write something about the number 943:

943 is the hypotenuse of a Pythagorean triple:
207-920-943 which is 23 times (9-40-41)

It is also a leg in two primitive Pythagorean triples:
576-943-1105, calculated from 2(32)(9), 32² – 9², 32² + 9²
943-444624-444625, calculated from 472² – 471², 2(472)(471), 472² + 471²

• 943 is a composite number.
• Prime factorization: 943 = 23 × 41
• 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 943 has exactly 4 factors.
• Factors of 943: 1, 23, 41, 943
• Factor pairs: 943 = 1 × 943 or 23 × 41
• 943 has no square factors that allow its square root to be simplified. √943 ≈ 30.708305

This puzzle is probably as tough as a level 1 puzzle can get, but don’t let that prevent you from giving it a try! Can you figure out where the factors from 1 to 12 go in both the first column and the top row?

Print the puzzles or type the solution on this excel file: 12 factors 942-950

Now let me tell you a little about the number 942:

It is the sum of four consecutive prime numbers:
229 + 233 + 239 + 241 = 942

It is the hypotenuse of a Pythagorean triple:
510-792-942 which is 6 times (85-132-157)

942 is a palindrome in two other bases and a repdigit in another:
787 in BASE 11, because 7(11²) + 8(11¹) + 7(11⁰) = 942
272 in BASE 20, because 2(20²) + 7(20¹) + 2(20⁰) = 942
666 in BASE 12, because 6(12²) + 6(12¹) + 6(12⁰) = 6(144+12+1) = 6(157) = 942

942³ is 835,896,888. OEIS.org tells us that 942³ is the smallest perfect cube that contains five 8‘s.

• 942 is a composite number.
• Prime factorization: 942 = 2 × 3 × 157
• 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 942 has exactly 8 factors.
• Factors of 942: 1, 2, 3, 6, 157, 314, 471, 942
• Factor pairs: 942 = 1 × 942, 2 × 471, 3 × 314, or 6 × 157
• 942 has no square factors that allow its square root to be simplified. √942 ≈ 30.6920185

Can you figure out where the factors 1 – 10 go in the first column and top row so that this level 5 puzzle will function as a multiplication table?

Print the puzzles or type the solution on this excel file: 10-factors-932-941

Now I’ll share a few facts about the number 938.

938 is a palindrome in two consecutive bases:
It’s 343 in BASE 17 because 3(17²) + 4(17¹) + 3(17º) = 938
It’s 2G2 in BASE 18 (G is 16 base 10), because 2(18²) + 16(18¹) + 2(18º) = 938

• 938 is a composite number.
• Prime factorization: 938 = 2 × 7 × 67
• 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 938 has exactly 8 factors.
• Factors of 938: 1, 2, 7, 14, 67, 134, 469, 938
• Factor pairs: 938 = 1 × 938, 2 × 469, 7 × 134, or 14 × 67
• 938 has no square factors that allow its square root to be simplified. √938 ≈ 30.62678566