How do you find the prime factorization of 72?

3 Answers
Aug 6, 2016

72 = 2^3xx3^2

Explanation:

Divide the number to be factored by the prime numbers in turn. Test that result is a natural number. If so, it is a prime factor. Continue until the factorisation is complete.

In this example:
72 is even so 2 is a factor; 72/2 = 36
36 and 36/2 = 18 are also even so we have two more 2's as prime factors.

18/2 = 9 = 3xx3 Hence we have two 3's as prime factors.

Therefore the prime factors of 72 are 2xx2xx2xx3xx3 =2^3xx3^2

Aug 6, 2016

The prime factorization for 72 is color(red)(2)xxcolor(red)(2)xxcolor(red)(2)xxcolor(red)(3)xxcolor(red)(3).

Explanation:

The prime factors are prime numbers that when multiplied result in the number that is being factored. Continually divide by prime numbers until you reach the last prime number.

Divide 72 by the prime number color(red)(2).

72/2=36

36xxcolor(red)2=72

Divide 36 by the prime number color(red)(2).

36/2=18

18xxcolor(red)2=36

Divide 18 by the prime number color(red)(2).

18/2=9

9xxcolor(red)2=18

Divide 9 by the prime number color(red)(3).

9/3=3

color(red)(3)xxcolor(red)3=9

The prime factorization for 72 is color(red)(2)xxcolor(red)(2)xxcolor(red)(2)xxcolor(red)(3)xxcolor(red)(3).

Aug 9, 2016

2^3xx3^2

Explanation:

If you are really stuck you can always draw a factor tree and see what you can build from than.

Tony BTony B

From this you can see that the prime factors are:

2^3xx3^2