What numbers have 6 identical prime factors?

Answer 1

There are two possible meanings for the question. One is what numbers have prime factorizations that are six of the same number, such as 2 x 2 x 2 x 2 x 2 x 2. One is what two or more numbers share six identical prime factors, such as 1260 and 12860, which share 2, 2, 3, 3, 5, and 7 as factors.

To find numbers that have the same Prime number repeated six times as a factor, choose a prime number and multiply six of them together; in other words, raise it to the sixth power.

26 = 2 x 2 x 2 x 2 x 2 x 2 = 64

36 = 3 x 3 x 3 x 3 x 3 x 3 = 729

56 = 5 x 5 x 5 x 5 x 5 x 5 = 15625

To find numbers that share the same six prime factors, choose any six prime factors and multiply them together. Then, multiply that number by two different prime numbers (or one of those numbers can be 1).

2 x 2 x 2 x 2 x 2 x 3 = 96

96 x 1 = 96

96 x 2 = 192

2 x 2 x 2 x 3 x 3 x 3 = 216

216 x 2 = 432

216 x 5 = 1080