6 — Factors and Prime Numbers

Factors and Prime Numbers

Solution & Explanation · ID: 37426924

Question

List all factors of 45.

Hint

Look for factor pairs that multiply to give 45.

Concept

Factors are numbers that divide evenly into another number. To find all factors, we test each number from 1 up to the given number to see which ones divide evenly.

Show Answer

1, 3, 5, 9, 15, 45

Show Solution
1

Start with 1: 45 ÷ 1 = 45 (no remainder), so 1 and 45 are factors.

2

Try 2: 45 ÷ 2 = 22.5 (has remainder), so 2 is not a factor.

3

Try 3: 45 ÷ 3 = 15 (no remainder), so 3 and 15 are factors.

4

Try 4: 45 ÷ 4 = 11.25 (has remainder), so 4 is not a factor.

5

Try 5: 45 ÷ 5 = 9 (no remainder), so 5 and 9 are factors.

6

We already found 9, and numbers beyond 9 would repeat pairs we've found.

A factor tree diagram showing 45 at the top. Below it are factor pairs connected by lines: (1,45), (3,15), and (5,9). Each pair is enclosed in a box. At the bottom, all factors are listed in order: 1, 3, 5, 9, 15, 45.