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=2×72

=2×2×36

=2×2×2×18

=2×2×2×2×9

=2×2×2×2×3×3

=24×32

Any positive factor of 144 can be expressed as:

2a×3b

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 5×3=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:

00010002000400080016

00030006001200240048

00090018003600720144

May 2, 2017

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

Explanation:

144=1144
144=272
144=348
144=436
144=624
144=818
144=916
144=1212

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=2432
5 possibilities to choose 20~4
3 possibilities to choose 30~2
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
= 2432

  1. Add 1 to each exponent:

= 24+132+1
= 2533

  1. Find the products of the exponents:

= 53
= 15

Best of luck!