What is the prime factorization of 96?

1 Answer
George C.
May 15, 2016

#96 = 2xx2xx2xx2xx2xx3 = 2^5*3#

Explanation:

Separate out each prime factor of #96# in turn.

We can tell that a number is divisible by #2# if its last digit is even.

So we find:

#96=2 xx 48#

#48=2 xx 24#

. . .

#6 = 2 xx 3#

We stop here since #3# is prime.

This process can be expressed using a factor tree:

#color(white)(00000)96#
#color(white)(0000)"/"color(white)(00)"\"#
#color(white)(000)2color(white)(000)48#
#color(white)(000000)"/"color(white)(00)"\"#
#color(white)(00000)2color(white)(000)24#
#color(white)(00000000)"/"color(white)(00)"\"#
#color(white)(0000000)2color(white)(000)12#
#color(white)(0000000000)"/"color(white)(00)"\"#
#color(white)(000000000)2color(white)(0000)6#
#color(white)(0000000000000)"/"color(white)(0)"\"#
#color(white)(000000000000)2color(white)(000)3#

So we find:

#96 = 2xx2xx2xx2xx2xx3 = 2^5*3#

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