Chapter 4.2, Problem 63E

To determine

To find prime factorisation of given number.

Answer to Problem 63E

2, 2, 13.

Explanation of Solution

Given Information:52

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 52, you divide 52 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 52. All the prime numbers that are used to divide in the Prime Factor Tree are the Prime Factors of 52. Here is the math to illustrate:

  $\begin{array}{l}52÷2=26\\ 26÷2=13\\ 13÷13=1\end{array}$

Again, all the prime numbers you used to divide above are the Prime Factors of 52. Thus, the Prime Factors of 52 are:

2, 2, 13.