How many factors does 144 have?

5 Answers
Mar 30, 2016

15 including 1.

Explanation:

Factors of 144 are {1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}#

i.e. in all 15 factors including 1.

Mar 30, 2016

15

Explanation:

To find the answer, first factor 144 into prime factors:

144=2 xx 72

=2 xx 2 xx 36

=2 xx 2 xx 2 xx 18

=2 xx 2 xx 2 xx 2 xx 9

=2 xx 2 xx 2 xx 2 xx 3 xx 3

=2^4 xx 3^2

Any positive factor of 144 can be expressed as:

2^a xx 3^b

where a = 0, 1, 2, 3, 4 and b = 0, 1, 2

That gives 5 possible values for a and 3 possible values for b and therefore 5 xx 3 = 15 factors.

Since there are only two distinct primes involved, we can write the factors in a grid with columns for the distinct powers of 2 and rows for the distinct powers of 3:

color(white)(000)1color(white)(000)2color(white)(000)4color(white)(000)8color(white)(00)16

color(white)(000)3color(white)(000)6color(white)(00)12color(white)(00)24color(white)(00)48

color(white)(000)9color(white)(00)18color(white)(00)36color(white)(00)72color(white)(0)144

May 2, 2017

it has 15 factors ={ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144}

Explanation:

144 = 1 * 144
144 = 2 * 72
144 = 3 * 48
144 = 4 * 36
144 = 6 * 24
144 = 8 * 18
144 = 9 * 16
144 = 12 * 12

it has 15 factors ={ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144}

May 2, 2017

15

Explanation:

there is another for you to observe @@
144=2^4*3^2
5 possibilities to choose 2^(0~4)
3 possibilities to choose 3^(0~2)
so
(4+1)*(2+1)=15

May 2, 2017

A = 15

Explanation:

The most accurate, yet the most complex method is first, prime decomposing and then using the exponent to calculate how many factors a set number x has! Furthermore, this method is extremely useful when calculating larger numbers rather than having to list out every single factor - a tiresome and boring process.

  1. Prime decompose the number:

= 144
= 2^4 * 3^2

  1. Add 1 to each exponent:

= 2^(4+1) * 3^(2+1)
= 2^5 * 3^3

  1. Find the products of the exponents:

= 5 * 3
= 15

Best of luck!