Step-by-Step Solution
117 = 3×3×13, so its factors are 1, 3, 9, 13, 39 and 117. The largest below 117 is 39, which you get by dividing 117 by its smallest prime factor, 3. The traps: 117 is a factor of itself but the question rules it out, 13 is a factor but a smaller one, and 59 does not divide 117 at all.
Answer: B) 39
Key idea: Factors come in pairs
To find every factor of a number, walk up from 1 and check each whole number — if it divides the number with no remainder, it is a factor. Factors come in **pairs**: if 4 is a factor of 12, so is 12 ÷ 4 = 3. So you only need to check up to the square root of the number to find them all. Factors of 12: 1×12,2×6,3×4 — six factors total: 1, 2, 3, 4, 6, 12. Every number has 1 and itself as factors.