A factor pair is a combination of two factors that can be multiplied together to equal a number.
Example Solution: 3 and 6, see solution.
Practice makes perfect
We want to write two numbers that have 18 and 30 as a multiple. To do so, recall that a factor pair is a combination of two factors that can be multiplied together to equal a number. Let's find the factor pairs of 18 and 30 by listing their factors!
Factor of18&: 1,2,3,6,9,18
Factor of30&: 1,2,3,5,6,10,15,30
We can write the factor pairs of each number by finding the product of two factors that equals 18 or 30.
Number
Product of Two Factors
Factor Pairs
18
1 * 18 =18 2 * 9 =18 3 * 6 =18
(1,18), (2,9), (3,6)
30
1 * 30 =30 2 * 15 =30 3 * 10 =30 5 * 6 = 30
(1,30), (2,15), (3,10), (5,6)
Remember that when a number is multiplied by an integer, the result is a multiple of the first number.
Note that the above products have the same form as the products we used to find the factor pairs. Then, we can list these products to identify the numbers that have 18 as a multiple. Let's do it!
1 * 18 &= 18 → 18 is multiple of 1
18 * 1 &= 18 → 18 is multiple of 18
2 * 9 &= 18 → 18 is multiple of 2
9 * 2 &= 18 → 18 is multiple of 9
3 * 6 &= 18 → 18 is multiple of 3
6 * 3 &= 18 → 18 is multiple of 6
Now let's do the same for the numbers that have 30 as a multiple.
1 * 30 &= 30 → 30 is multiple of 1
30 * 1 &= 30 → 30 is multiple of 30
2 * 15 &= 30 → 30 is multiple of 2
15 * 2 &= 30 → 30 is multiple of 15
3 * 10 &= 30 → 30 is multiple of 3
10 * 3 &= 30 → 30 is multiple of 10
5 * 6 &= 30 → 30 is multiple of 5
6 * 5 &= 30 → 30 is multiple of 6
Notice that 18 and 30 are common multiples for 1, 2, 3, and 6. Therefore, 3 and 6 are two numbers that have 18 and 30 as multiples. Notice that this is only a possible answer, as there are more numbers with 18 and 30 as multiples.
