How do you find the prime factorization on 75?

Question

15944 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-11T00:55:07

Divide by prime factors to find that

$75 = 3 \times 5 \times 5 = 3 \times 5^{2}$ $75 = 3xx5xx5 = 3xx5^2$

The simplest way of finding the prime factorization of an integer is to divide by prime factors until the result is a prime.

First, we can see that $75$ $75$ is divisible by $5$ $5$ , as it ends in $5$ $5$ . Dividing, we get

$75 \div 5 = 15$ $75 -: color(red)(5) = 15$

Next, $15$ $15$ is also divisible by $5$ $5$ , so we divide again.

$15 \div 5 = 3$ $15 -: color(red)(5) = 3$

Finally, $3$ $3$ is a prime number, so it, together with the divisors in the prior steps, form the prime factorization of $75$ $75$ .

$75 = 3 \times 5 \times 5$ $75 = 3xx5xx5$

Answer 2 · 2017-01-11T00:55:07

Keep on trying to divide by the primes in succession:

2 doesn't go into 75
3 does: $75 = 3 \times 25$ $75=3xx25$
another 3 doesn't go into 25
5 does: $75 = 3 \times 5 \times 5$ $75=3xx5xx5$

And there it ends, because the last $5$ $5$ is also prime.