How many factors does 144 have?

Question

Mila Anderson · Accepted Answer

#15# including #1#.

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#.

Cameron Arnold · Answer

#15# 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#

Luna Angel · Answer

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

#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}

Aurora Arias · Answer

15

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#

Noah Archer · Answer

A = #15#

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.

= #144# = #2^4 * 3^2#

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

= #5 * 3# = #15#

Wishing you luck!

Gianna Caruso · Answer

undefined The number 144 has 15 factors.