What is the prime factorization of 45?

Question

Mila Anderson · Accepted Answer

#45 = 5 * 3*3#.

This could also be written as: #5 *3^2# From the multiplication table, we know that #45 = 5 * 9#. #5# is prime, but #9# is not. The prime factorization of #9# is #3*3#, so the prime factorization of #45# is #45 = 5 * 3*3# --or-- #5 *3^2#. Whole numbers that can only be divided by one and themselves are known as prime numbers. The first primes are: #2, 3, 5, 7, 11, 13, 17, 19, 23, ... # (#2# is the ONLY even prime number. All the rest are odd.) Getting a prime factorization involves: First, determine whether the number you need to factor can be divided by 2, 3, or 5. If so, divide it by that prime and see what's left. Next, determine whether the remaining number can also be divided by 2, 3, or 5. Finally, continue in this manner until you have a (multiplied) list of 2s, 3s, and 5s. You can move on to the next prime, which is 7, if your number cannot be divided by 2, 3, or 5. Proceed to number eleven and continue trying the known small primes in order until you have a factorization that is made up entirely of prime numbers if the remaining factor of the original number is still not prime. There are a ton of useful websites regarding prime numbers. Check out these: Mathforum.org/dr.math/faq/faq.prime.num.html Mathsisfun.com/prime_numbers.html (The Prime Numbers page on Wikipedia is extremely intricate.) At https://tutor.hix.ai Khan Academy offers some great videos covering math topics. Number theory includes the study of prime numbers. Enjoy your time with them!

Riley Anderson · Answer

undefined The prime factorization of 45 is 3 x 3 x 5.