# 627 and Level 5

Here are two divisibility rules applied to 627 that give a positive result:

• 6 + 2 + 7 = 15, a multiple of 3, so 627 is divisible by 3.
• 6 – 2 + 7 = 11, so 627 is divisible by 11.

627 can be expressed as the sum of consecutive counting numbers 4 different ways. The numbers in bold are in the middle of each sum:

• 208 + 209 + 210 = 627
• 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 + 61 + 62 = 627
• 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 = 627
• 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11+ 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 + 31 + 32 + 33 + 34 + 35 = 627

The logic on this Level 5 puzzle gets a bit complicated right when it’s almost done: Print the puzzles or type the solution on this excel file: 12 Factors 2015-09-21

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• 627 is a composite number.
• Prime factorization: 627 = 3 x 11 x 19
• 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 x 2 x 2 = 8. Therefore 627 has exactly 8 factors.
• Factors of 627: 1, 3, 11, 19, 33, 57, 209, 627
• Factor pairs: 627 = 1 x 627, 3 x 209, 11 x 57, or 19 x 33
• 627 has no square factors that allow its square root to be simplified. √627 ≈ 25.039968. ————————————————————————————————— This site uses Akismet to reduce spam. Learn how your comment data is processed.