How many factors does 144 have?

5 Answers
Mar 30, 2016

1515 including 11.

Explanation:

Factors of 144144 are {1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}#

i.e. in all 1515 factors including 11.

Mar 30, 2016

1515

Explanation:

To find the answer, first factor 144144 into prime factors:

144=2 xx 72144=2×72

=2 xx 2 xx 36=2×2×36

=2 xx 2 xx 2 xx 18=2×2×2×18

=2 xx 2 xx 2 xx 2 xx 9=2×2×2×2×9

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

=2^4 xx 3^2=24×32

Any positive factor of 144144 can be expressed as:

2^a xx 3^b2a×3b

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

That gives 55 possible values for aa and 33 possible values for bb and therefore 5 xx 3 = 155×3=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 22 and rows for the distinct powers of 33:

color(white)(000)1color(white)(000)2color(white)(000)4color(white)(000)8color(white)(00)1600010002000400080016

color(white)(000)3color(white)(000)6color(white)(00)12color(white)(00)24color(white)(00)4800030006001200240048

color(white)(000)9color(white)(00)18color(white)(00)36color(white)(00)72color(white)(0)14400090018003600720144

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 * 144144=1144
144 = 2 * 72144=272
144 = 3 * 48144=348
144 = 4 * 36144=436
144 = 6 * 24144=624
144 = 8 * 18144=818
144 = 9 * 16144=916
144 = 12 * 12144=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=2^4*3^2144=2432
5 possibilities to choose 2^(0~4)20~4
3 possibilities to choose 3^(0~2)30~2
so
(4+1)*(2+1)=15(4+1)(2+1)=15

May 2, 2017

A = 1515

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 xx 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:

= 144144
= 2^4 * 3^22432

  1. Add 11 to each exponent:

= 2^(4+1) * 3^(2+1)24+132+1
= 2^5 * 3^32533

  1. Find the products of the exponents:

= 5 * 353
= 1515

Best of luck!