How do I express 108 as a product of prime factors?

Question

Gabriel Agustin · Accepted Answer

#108=2xx2xx3xx3xx3=2^2xx3^3#

split the number into a product pair with at least one of them being prime. Then split the non-prime number into a product pair again. Continue until all the factors are prime numbers.

#108=color(blue)(2)xx54#

#108=2xxcolor(blue)(2)xx27#

#108=2xx2xxcolor(blue)(3)xx9#

#108=2xx2xx3xx3xx3#

#108=2xx2xx3xx3xx3=2^2xx3^3#

Jeremiah Andrews · Answer

#108 = 2^2 xx 3^3# You can start with any two factors of #108# and break them into smaller and smaller factors, until they are all prime numbers, #108 = " "12 " "xx 9# #108 = 4xx3" "xx3xx3# #108 = 2xx2xx3xx3xx3# #108 = 2^2 xx 3^3#

Luna Angel · Answer

#2^2 xx 3^3= 108#

Search for all the primes it's divisible by.

As it is even, it is divisible by 2.

#108/2=54#

54 is also divisible by 2.

#108/2^2=54/2=27#

You may recognize 27 as being equal to #3^3#. (If you get a less obvious number then you can simply guess primes smaller than this until you find one that divides it or use division algorithms etc).

So, we divided 108 by #2^2# and #3^3# which gives us #1#.

These two numbers are powers of primes that when multiplied give us 108:

#2^2 xx 3^3= 108#

Luna Angel · Answer

undefined To express 108 as a product of prime factors, you would divide it by the smallest prime number, 2, and continue dividing by prime numbers until you reach 1. The prime factorization of 108 is 2^2 × 3^3.