# 1175 and Level 2

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