How do you find the prime factorization on 75?

Question

Noah Archer · Accepted Answer

Divide by prime factors to find that

#75 = 3xx5xx5 = 3xx5^2# Dividing an integer by its prime factors until the result is a prime is the simplest method for determining its prime factorization. First, we can see that #75# is divisible by #5#, as it ends in #5#. Dividing, we get #75 -: color(red)(5) = 15# Next, #15# is also divisible by #5#, so we divide again. #15 -: color(red)(5) = 3# Finally, #3# is a prime number, so it, together with the divisors in the prior steps, form the prime factorization of #75#. #75 = 3xx5xx5#

Noah Archer · Answer

Keep on trying to divide by the primes in succession:

2 doesn't go into 75 3 does: #75=3xx25# another 3 doesn't go into 25 5 does: #75=3xx5xx5# And there it ends, because the last #5# is also prime.

Aurora Arias · Answer

undefined To find the prime factorization of 75, you can follow these steps:

1. Begin by dividing the number by the smallest prime number, which is 2.
2. Since 75 is not divisible by 2, move on to the next smallest prime number, which is 3.
3. Divide 75 by 3. 75 ÷ 3 = 25.
4. Now, you need to determine if 25 is divisible by 3. It is not, so proceed to the next prime number.
5. The next prime number to check is 5. Divide 25 by 5. 25 ÷ 5 = 5.
6. Since 5 is a prime number, you have completed the factorization process.
7. Write down the prime factors: 3 × 5 × 5.

Therefore, the prime factorization of 75 is 3 × 5 × 5, or written in exponential form: $3^1 \times 5^2$.