Some of the clues in this level 2 puzzle were also in the level 1 puzzle earlier this week. Can you remember their common factors and figure out the common factors for the other three sets of clues?

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

Here are some facts about the number 1189:

• 1189 is a composite number.
• Prime factorization: 1189 = 29 × 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 1189 has exactly 4 factors.
• Factors of 1189: 1, 29, 41, 1189
• Factor pairs: 1189 = 1 × 1189 or 29 × 41
• 1189 has no square factors that allow its square root to be simplified. √1189 ≈ 34.48188

33² + 10² = 1189
30² + 17² = 1189

1189 is the hypotenuse of FOUR Pythagorean triples:
261-1160-1189 which is 29 times (9-40-41)
611-1020-1189 calculated from 30² – 17², 2(30)(17), 30² + 17²
660-989-1189 calculated from 2(33)(10), 33² – 10², 33² + 10²
820-861-1189 which is (20-21-29) times 41

1189 is 10010100101 in BASE 2. That’s a nice pattern.
It’s also palindrome 1H1 in base 27 ( H is 17 base 10),
and palindrome 131 in BASE 33

Every Find the Factors puzzle I make has a unique solution. That fact is central to the logic needed to begin this particular puzzle. I hope it frustrates you a little, but not too much. Then when you finally solve it, it will be so much sweeter!

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

Here are some facts about the number 1182:

• 1182 is a composite number.
• Prime factorization: 1182 = 2 × 3 × 197
• 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 1182 has exactly 8 factors.
• Factors of 1182: 1, 2, 3, 6, 197, 394, 591, 1182
• Factor pairs: 1182 = 1 × 1182, 2 × 591, 3 × 394, or 6 × 197
• 1182 has no square factors that allow its square root to be simplified. √1182 ≈ 34.38023

1182 is the hypotenuse of a Pythagorean triple:
168-1170-1182 which is 6 times (28-195-197)

1182 is a palindrome in two bases:
It’s 606 in BASE 14 because 6(14²) + 6(1) = 6(197) = 1182,
and 2J2 in BASE 20 (J is 19 base 10) because 2(20²) + 19(20) + 2(1) = 1182

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.