80 and 16 have just one common factor that will put only numbers from 1 to 10 in the first column and in the top row. Put those factors where they belong and use logic to figure out where to put the rest.

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

Now I tell you what I’ve learned about the number 1179:

• 1179 is a composite number.
• Prime factorization: 1179 = 3 × 3 × 131, which can be written 1179 = 3² × 131
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 1179 has exactly 6 factors.
• Factors of 1179: 1, 3, 9, 131, 393, 1179
• Factor pairs: 1179 = 1 × 1179, 3 × 393, or 9 × 131
• Taking the factor pair with the largest square number factor, we get √1179 = (√9)(√131) = 3√131 ≈ 34.33657

I like the way 1179 looks in a couple other bases:
It’s 2233 in BASE 8 because 2(8³ + 8²) + 3(8 + 1) = 1179,
and 171 in BASE 31 because 31² + 7(31) + 1 = 1179

Why are two of the clues in today’s level three puzzle in red?

You still figure out the common factor of 32 and 72, then work down the first column cell by cell filling in factors as you go, BUT you won’t be able to know what factors to use for 9 unless you look at the number 15 first. You don’t have a problem with that, do you?

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

Now I’ll tell you some facts about the number 1177:

• 1177 is a composite number.
• Prime factorization: 1177 = 11 × 107
• 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 1177 has exactly 4 factors.
• Factors of 1177: 1, 11, 107, 1177
• Factor pairs: 1177 = 1 × 1177 or 11 × 107
• 1177 has no square factors that allow its square root to be simplified. √1177 ≈ 34.30743

1177 is a palindrome in two bases:
It’s 414 in BASE 17 because 4(17²) + 1(17) + 4(1) = 1177
and 1E1 in BASE 28 (E is 14 base 10) because 28² + 14(28) + 1 = 1177

This level 2 puzzle will be quite useful in helping you recall all the multiplication facts. How many factors can you fill in on this puzzle without looking at a regular multiplication table? I congratulate you on all the ones you know.

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

Here are some facts about the number 1175:

• 1175 is a composite number.
• Prime factorization: 1175 = 5 × 5 × 47, which can be written 1175 = 5² × 47
• The exponents in the prime factorization are 2 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 × 2  = 6. Therefore 1175 has exactly 6 factors.
• Factors of 1175: 1, 5, 25, 47, 235, 1175
• Factor pairs: 1175 = 1 × 1175, 5 × 235, or 25 × 47
• Taking the factor pair with the largest square number factor, we get √1175 = (√25)(√47) = 5√47 ≈ 34.27827

1175 is the hypotenuse of two Pythagorean triples:
705-940-1175 which is (3-4-5) times 235
329-1128-1175 which is (7-24-25) times 47

1175 is a palindrome in these other bases:
It’s 979 in BASE 11 because 9(11²) + 7(11) + 9(1) = 1175,
535 in BASE 15 because 5(15²) + 3(15) + 5(1) = 1175,
and 252 in BASE 23 because 2(23²) + 5(23) + 2(1) = 1175

I’ve given you just nine clues in this puzzle, but that’s enough to find all the factors AND complete the entire table. I’m serious. I really have given you sufficient information to find the one and only solution to this puzzle!

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

Now I’ll share some information about the number 1174:

• 1174 is a composite number.
• Prime factorization: 1174 = 2 × 587
• 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 1174 has exactly 4 factors.
• Factors of 1174: 1, 2, 587, 1174
• Factor pairs: 1174 = 1 × 1174 or 2 × 587
• 1174 has no square factors that allow its square root to be simplified. √1174 ≈ 34.26368

1174 is also the sum of the sixteen prime numbers from 41 to 107.

The twelve clues in this puzzle make an attractive puzzle for you to solve. What factors go with those clues? Can you find the logic needed to figure this one out?

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

Now I’ll share what I’ve learned about the number 1169:

• 1169 is a composite number.
• Prime factorization: 1169 = 7 × 167
• 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 1169 has exactly 4 factors.
• Factors of 1169: 1, 7, 167, 1169
• Factor pairs: 1169 = 1 × 1169 or 7 × 167
• 1169 has no square factors that allow its square root to be simplified. √1169 ≈ 34.19064

1169 is the sum of consecutive prime numbers two different ways:
227+ 229 + 233+ 239+ 241 = 1169
383+ 389 + 397 = 1169

1169 is palindrome 5225 in BASE 6 because 5(6³) + 2(6²) + 2(6) + 5(1) = 1169

Will some of the tricky clues in this level 5 puzzle fool you? They won’t if you only write factors of which you are 100% sure. Always use logic. Never guess and check.

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

Now I’ll write a little bit about the number 1167:

• 1167 is a composite number.
• Prime factorization: 1167 = 3 × 389
• 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 1167 has exactly 4 factors.
• Factors of 1167: 1, 3, 389, 1167
• Factor pairs: 1167 = 1 × 1167 or 3 × 389
• 1167 has no square factors that allow its square root to be simplified. √1167 ≈ 34.16138

1167 is the hypotenuse of a Pythagorean triple:
567-1020-1167 which is 3 times (189-340-389)

1167 is palindrome 5D5 in BASE 14 (D is 13 base 10)
because 5(14²) + 13(14) + 5(1) = 1167