Some of the clues in this puzzle pair up in the same column or the same row and try to trick you into picking the wrong common factor. Nevertheless, the 10 clues in the puzzle work together to give you the most logical place to start the puzzle. It may be a little difficult to see the logic for this one but stick with it. You’ll figure it out.

Print the puzzles or type the solution in this excel file: 10-factors-1002-1011

Here’s a little bit about the number 1007:

1007 is the hypotenuse of a Pythagorean triple:
532-855-1007lwhich is 19 times (28-45-53)

1007 is palindrome 33233 in BASE 4
because 3(4⁴) + 3(4³) + 2(4²) + 3(4¹) + 3(4⁰) = 1007

• 1007 is a composite number.
• Prime factorization: 1007 = 19 × 53
• 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 1007 has exactly 4 factors.
• Factors of 1007: 1, 19, 53, 1007
• Factor pairs: 1007 = 1 × 1007 or 19 × 53
• 1007 has no square factors that allow its square root to be simplified. √1007 ≈ 31.73326

There is only one multiplication table that has the numbers you see in this puzzle exactly where you see them here. Can you find the factors that create that multiplication table? This is a level 6 puzzle so it won’t be easy, but it can be done by just using logic and the basic 1-12 multiplication facts.

Print the puzzles or type the solution in this excel file: 12 factors 993-1001

1001 is the product of three consecutive prime numbers:
7 × 11 × 13 = 1001

1001 is also the sum of fifteen consecutive prime numbers:
37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 = 1001

1001 is the 26th pentagonal number.

1001 is the hypotenuse of a Pythagorean triple:
385² + 924² = 1001²

1001 is a palindrome in base 10 and in base 25:
It’s 1F1 in BASE 25 (F is 15 base 10) because 1(625) + 15(25) + 1(1) = 1001

• 1001 is a composite number.
• Prime factorization: 1001 = 7 × 11 × 13
• 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 1001 has exactly 8 factors.
• Factors of 1001: 1, 7, 11, 13, 77, 91, 143, 1001
• Factor pairs: 1001 = 1 × 1001, 7 × 143, 11 × 91, or 13 × 77
• 1001 has no square factors that allow its square root to be simplified. √1001 ≈ 31.63858

This puzzle is a multiplication table. You don’t have to be fast to solve it, but you do have to think. There is only one solution. The ten clues given are sufficient to find the places to put the factors 1 to 10 in the first column and the top row. Good luck!

Print the puzzles or type the solution in this excel file: 10-factors-951-958

958 is the sum of the 22 prime numbers from 5 to 89.

958 is also 141 in BASE 29 because 1(29²) + 4(29¹) + 1(29⁰) = 958

• 958 is a composite number.
• Prime factorization: 958 = 2 × 479
• 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 958 has exactly 4 factors.
• Factors of 958: 1, 2, 479, 958
• Factor pairs: 958 = 1 × 958 or 2 × 479
• 958 has no square factors that allow its square root to be simplified. √958 ≈ 30.951575

Today’s puzzle is a level 6, so it isn’t for beginners. It is trickier than the easier levels, but don’t let that stop you from giving it a try. If you use guess and check, you will likely become frustrated, but you can solve this puzzle IF you use logic before you write each factor.

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

950 is the hypotenuse of two Pythagorean triples:
266-912-950 which is (7-24-25) times 38
570-760-950 which is (3-4-5) times 190

950 is 2525 in BASE 7 because 2(7³) + 5(7²) + 2(7¹) + 5(7⁰) = 950

• 950 is a composite number.
• Prime factorization: 950 = 2 × 5 × 5 × 19, which can be written 950 = 2 × 5² × 19
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 950 has exactly 12 factors.
• Factors of 950: 1, 2, 5, 10, 19, 25, 38, 50, 95, 190, 475, 950
• Factor pairs: 950 = 1 × 950, 2 × 475, 5 × 190, 10 × 95, 19 × 50, or 25 × 38,
• Taking the factor pair with the largest square number factor, we get √950 = (√25)(√38) = 5√38 ≈ 30.82207

This witch’s broom is a puzzle based on the multiplication table. The factors from 1 to 12 are out of order in the first column and the top row, but they all belong somewhere in each place. Use logic to figure out where those factors go. It’s a level 6, so it will be a little tricky, but not as tricky as it sometimes is. Solve it, and you might feel like flying!

Print the puzzles or type the solution on this excel file: 12 factors 923-931

What is special about the number 930?

463 + 467 = 930, so it is the sum of consecutive prime numbers.

30 × 31 = 930 The factors in that factor pair are consecutive so 930 is the sum of the first 30 EVEN numbers:
2 + 4 + 6 + 8 + . . . + 54 + 56 + 58 + 60 = 930

930 is the hypotenuse of a Pythagorean triple:
558-744-930, which is (3-4-5) times 186.

Here’s 930 in a few other bases:
Palindrome 656 in BASE 12, because 6(144) + 5(12) + 6(1) = 930
110 in BASE 30, because 1(30²) + 1(30) + 0(1) = 30(31) = 930
U0 in BASE 31 (U is 30 base 10), because 30(31) + 0(1) = 930

• 930 is a composite number.
• Prime factorization: 930 = 2 × 3 × 5 × 31
• 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 = 16. Therefore 930 has exactly 16 factors.
• Factors of 930: 1, 2, 3, 5, 6, 10, 15, 30, 31, 62, 93, 155, 186, 310, 465, 930
• Factor pairs: 930 = 1 × 930, 2 × 465, 3 × 310, 5 × 186, 6 × 155, 10 × 93, 15 × 62, or 30 × 31
• 930 has no square factors that allow its square root to be simplified. √930 ≈ 30.495901.