How many factors does 144 have?

5 Answers
Mar 30, 2016

Answer:

#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

Answer:

#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

Answer:

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

Answer:

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

Answer:

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!