How do you make a factor tree for 189?

Answer 1

First, find two numbers that when multiplied together equal 189.

I can tell by looking at the number that it is divisible by 9. Any number whose digits add up to a number divisible by 9 is also divisible by 9. 1 + 8 + 9 = 18, which is divisible by 9. 189 ÷ 9 is 21.

So, the top of our factor tree is:

189

9 x 21

Now, determine two pairs of numbers that when multiplied together, one pair will equal 9 and the other pair will equal 21. 9 = 3 x 3 and 21 = 7 x 3.

So, now our factor tree is:

189

9 x 21

(3x3) x (7x3)

You would continue doing this until you no more numbers can be factored. Since 3 and 7 are prime numbers, the factor tree is finished.

The factor tree shows that the prime factorization of 189 is 3 x 3 x 3 x 7 or 33 x 7.