How do you create a factor tree for 204?

Question

Mila Anderson · Accepted Answer

See explanation...

#color(white)()# #color(white)(00000)204# #color(white)(0000)"/"color(white)(000)"\"# #color(white)(000)2color(white)(0000)102# #color(white)(0000000)"/"color(white)(000)"\"# #color(white)(000000)2color(white)(0000)51# #color(white)(0000000000)"/"color(white)(00)"\"# #color(white)(000000000)3color(white)(000)17# #204 = 2 xx 102# #color(white)()# * #102# ends with an even digit, so we can tell that it's divisible by #2#... #102 = 2 xx 51# #color(white)()# * #51# ends in an odd digit, so is not divisible by #2#, but the sum of its digits is #5+1 = 6#, which is divisible by #3#. So we can tell that #51# is divisible by #3#... #51 = 3 xx 17# #color(white)()# * #17# is a prime number, so stop.

Roman Alvarez · Answer

undefined To create a factor tree for 204, you start by breaking it down into its prime factors:

204 = 2 * 102

Now, we continue breaking down 102:

102 = 2 * 51

Breaking down 51:

51 = 3 * 17

Since both 3 and 17 are prime numbers, we stop here.

So, the prime factorization of 204 is:

204 = 2 * 2 * 3 * 17

To represent this as a factor tree:

204
  /     \
2       102
        /     \
      2        51
             /     \
           3       17