30.5k views
0 votes
Find a number with six factors, all of which are odd numbers

User Djreed
by
3.9k points

2 Answers

2 votes

Answer:

45

Explanation:

1,3,5,9,15,45

User Fresh
by
4.1k points
7 votes

9514 1404 393

Answer:

  • 45 has divisors 1, 3, 5, 9, 15, 45
  • 75 has divisors 1, 3, 5, 15, 25, 75

Explanation:

The number of divisors a number has is the product of the powers of its prime factors, each increased by 1. If a number has 6 factors, it will be either the 5th power of an odd prime, or the product of two odd primes, one of them being squared.

Examples:

243 = 3^5 has 5+1 = 6 divisors: 1, 3, 9, 27, 81, 243

45 = 3^2×5 has (2+1)(1+1) = 6 divisors: 1, 3, 5, 9, 15, 45

75 = 3×5^2 has (1+1)(2+1) = 6 divisors: 1, 3, 5, 15, 25, 75

331169 = 61^2×89 has (2+1)(1+1) = 6 divisors: 1, 61, 89, 3721, 5429, 331169

User SergeantPenguin
by
4.0k points