Examples and questions on how to find factors and multiples of whole numbers , with detailed solutions and explanations, for grade 6 students are presented.
Division and multiplication are related operations.
The division 6 ÷ 3 = 2 (with remainder equal to 0) may be written as the multiplication: 6 = 2 × 3
The division 15 ÷ 3 = 5 (with remainder equal to 0) may be written as the multiplication: 15 = 5 × 3
The multiplication: 10 = 2 × 5 may be written as the division: 10 ÷ 5 = 2 (with remainder equal to 0)
The multiplication: 18 = 6 × 3 may be written as the division: 18 ÷ 3 = 6 (with remainder equal to 0)
Examples
1) 6 = 1 × 6 ; 6 = 2 × 3 1, 2, 3 and 6 are called factors of 6.
2) 12 = 12 ×1 = 3 × 4 = 6 ×2 1, 2, 3, 4, 6 and 12 are called factors of 12.
3) 20 = 1 × 20 = 2 × 10 = 2 × 2 × 5 = 4 × 5 1, 2, 3, 4, 5, 10 and 20 are called factors of 20.
Examples
Find all factors of 30
Divide 30 by all numbers starting from 1 and select the division that gives a remainder equal to 0 then write the factors.
30 ÷ 1 = 30 remainder 0 or 30 = 30 × 1. Hence 1 and 30 are factors
30 ÷ 2 = 15 remainder 0 or 30 = 15 × 2 . Hence both 2 and 15 are factors
30 ÷ 3 = 10 remainder 0 or 30 = 10 × 3 . Hence both 3 and 10 are factors
30 ÷ 4 = 7 remainder 2 , 4 is not a factor
30 ÷ 5 = 6 remainder 0 or 30 = 6 × 5 . Hence both 5 and 6 area factors.
We stop here because all factors greater that 5 have already been found.
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
Take a whole number and multiply it by 1, 2, 3, 4, ... to obtain the multiples as follows:
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 4 = 20
The results of the multiplication of 5 by 1, 2, 3, 4, ... which are 5, 10, 15, 20, ... are called the multiples of 5.
FALSE 4 ÷ 2 = 2 with remainder 0
TRUE 9 = 3 × 3
TRUE 15 = 5 × 3
FALSE There is no whole number N such that 7 = 3 × N
TRUE 10 ÷ 10 = 1 with remainder equal to 0.
TRUE 16 = 16 × 1
TRUE N = N × 1
TRUE N = N × 1 , at least two factors 1 and N (itself)
2 ÷ 1 = 2 with remainder 0 or 2 = 2 × 1 . Hence the factors of 2 are 1 and 2.
6 ÷ 1 = 6 with remainder 0 or 6 = 6 × 1. Two factors 1 and 6.
6 ÷ 2 = 3 with remainder 0 or 6 = 3 × 2. Two factors 2 and 3.
All factors greater than 2 already found, we stop the division process and write the list of factors of 6 are 1, 2, 3 and 6.
10 ÷ 1 = 10 with remainder 0 or 10 = 10 × 1. Two factors 1 and 10.
10 ÷ 2 = 5 with remainder 0 or 10 = 5 × 2. Two factors 2 and 5.
10 ÷ 3 = 3 with remainder 1; 3 is not a factor of 10.
10 ÷ 4 = 2 with remainder 2; 4 is not a factor 10.
All factors greater that 4 already found, we stop the division process and write the list of factors 10 are 1, 2, 5 and 10.
24 ÷ 1 = 24 with remainder 0 or 24 = 24 × 1. Two factors 1 and 24.
24 ÷ 2 = 12 with remainder 0 or 24 = 12 × 2. Two factors 2 and 12.
24 ÷ 3 = 8 with remainder 0 ; or 24 = 8 × 3. Two factors 3 and 8.
24 ÷ 4 = 6 with remainder 0; or 24 = 6 × 4. Two factors 4 and 6.
24 ÷ 5 = 4 with remainder 4; no factors.
All factors greater that 5 already found, we stop the division process and write the list of factors 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
120 ÷ 2 = 60 with remainder 0 , 2 is a factor of 120
120 ÷ 5 = 24 with remainder 0 , 5 is a factor of 120
120 ÷ 10 = 12 with remainder 0 , 10 is a factor of 120
120 ÷ 11 = 10 with remainder 10 , 11 is NOT a factor of 120
120 ÷ 20 = 6 with remainder 0 , 20 is a factor of 120
120 ÷ 30 = 4 with remainder 0 , 30 is a factor of 120
120 ÷ 50 = 2 with remainder 20 , 50 is NOT a factor of 120
In the given list all are factors of 120 except 11 and 50.
We first find all factors of 12
12 ÷ 1 = 12 with remainder 0 , 1 and 12 are factors of 12
12 ÷ 2 = 6 with remainder 0 , 2 and 6 are factors of 12
12 ÷ 3 = 4 with remainder 0 , 3 and 4 are factors of 12
All factors greater that 3 already found, we stop the division process and write the list of factors of 12: 1, 2, 3, 4, 6 and 12.
The factors of 24 were found in solution to 2) part d) and are given by
1, 2, 3, 4, 6, 8, 12 and 24
Common factors to 12 and 24 are: 1, 2, 3, 4, 6 and 12.
The first 5 mutliples mutliples of a number are obtained by multiplying that number by 1, 2, 3, 4 and 5
2 × 1 = 2
2 × 2 = 4
2 × 3 = 6
2 × 4 = 8
2 × 5 = 10
11 × 1 = 11
11 × 2 = 22
11 × 3 = 33
11 × 4 = 44
11 × 5 = 55
25 × 1 = 25
25 × 2 = 50
25 × 3 = 75
25 × 4 = 100
25 × 5 = 125
The first 5 mutliples mutliples of 6 and 8 number are obtained by multiplying 6 and 8 by 1, 2, 3, 4 and 5
6 × 1 = 6
6 × 2 = 12
6 × 3 = 18
6 × 4 = 24
6 × 5 = 30
8 × 1 = 11
8 × 2 = 16
8 × 3 = 24
8 × 4 = 32
8 × 5 = 40
24 is a common multiple to 6 and 8