Chapter 4.2, Problem 61E

To determine

To find prime factorisation of given number.

Answer to Problem 61E

5, 5, 5.

Explanation of Solution

Given Information:125

Formula used: The prime factors of a number are all the prime numbers that, when multiplied together, equal the original number. You can find the prime factorisation of a number by using a factor tree and dividing the number into smaller parts.

Calculation:

To get the Prime Factors of 125, you divide 125 by the smallest prime number possible. Then you take the result from that and divide that by the smallest prime number. Repeat this process until you end up with 1.

This Prime Factorization process creates the Prime Factor Tree of 125. All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 125. Here is the math to illustrate:

  $\begin{array}{l}125÷5=25\\ 25÷5=5\\ 5÷5=1\end{array}$

Again, all the prime numbers you used to divide above are the Prime Factors of 125. Thus, the Prime Factors of 125 are:

5, 5, 5.