Oh, dude, the positive difference between the number of distinct prime factors of 15 squared (225) and 64 cubed (262,144) is like 4. Prime factors are like those VIP numbers that can't be divided by anything except 1 and themselves. So, 225 has 2 distinct prime factors (3 and 5), and 262,144 has 1 distinct prime factor (2). Subtract 1 from 2, and you get 1. Wow, math can be fun, right?
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The number 152 can be factored into 2 x 2 x 3 x 5, which has 3 distinct prime factors. The number 643 can be factored into 2 x 2 x 2 x 2 x 2 x 2 x 2, which has 1 distinct prime factor. Therefore, the positive difference between the number of distinct prime factors of 152 and 643 is 3 - 1 = 2.
The definition of a prime is an integer that has two positive factors, one and itself. These are two distinct factors. One only has one positive factor. Thus it's not a prime.
Twelve distinct factors.
Proper factors do not include one and the number itself.
Three distinct prime factors.
Factors go into the number. The number goes into multiples.