How many odd factors does 210 have?

Answer 1

Step 1: Prime Factorization - every factor of any given number can be constructed from its prime factorization

1. 210 = 210 = 21 * 10 = 7 * 3 * 5 * 2 (and * 1)

Step 2: Properties of Odd Numbers - through logic or trial/error you can determine that an odd number can only be made by multiplying two odd numbers (odd * even and even * even both result in even numbers always)

1. Combine any odd numbers from the prime factorizations
2. 7 * 3 = 21, 7 * 5 = 35, 3 * 5 = 15, and don't forget 7 * 3 * 5 = 105

Step 3: Count All Odd Factors

1. 1, 3, 5, 7, 15, 21, 35, 105 = 8 total

Traps: Don't forget 1 and 105