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5th Grade Factors and Multiples
Here we will discuss how factors and multiples are related to each other in math.
Definition of Factor:
A factor of a number is a divisor which divides the dividend exactly.
For example,
2 is a factor of 6, 3 is a factor of 12 etc.
Let us consider some more examples.
1. Write all the factors of 36.
Solution:
All the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
A factor of a number which is a prime number is called a prime factor.
For example, 3 is a prime factor of 36.
2. Find the prime factor of 312.
Solution:
Therefore, the prime factors of 312 are 2 x 2 x 2 x 3 x 13.
Definition of Multiple:
A multiple of a number is the product of the number and a whole number.
For example, multiples of 4 are 4, 8, 12, 16, 20, etc.
Here 4 is the product of 4 and 1.
Similarly, 8 is the product of 4 and 2 and 12 is the product of 4 and 3 and so on.
Let us consider an example.
1. Find the first five multiples of 24 except itself.
Solution:
The first five multiples of 24 are
24 x 2 = 48,
24 x 3 = 72,
24 x 4 = 96,
24 x 5 = 120,
24 x 6 = 144
Remember:
The factors of a number are always limited but the multiples of a number are unlimited.
For example, 16 has only 5 factors 1, 2, 4, 8, 16 but its multiples are unlimited — 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, ...
Worksheet on 5th Grade Factors and Multiples
I. Find all the factors of the following other than 1.
1. 36
2. 48
3. 64
4. 75
5. 124
6. 150
7. 169
8. 175
9. 210
Answer:
I. 1. 2, 3, 4, 6, 9, 12, 18, 36
2. 2, 3, 4, 6, 8, 12, 16, 24, 48
3. 2, 4, 8, 16, 32, 64
4. 5, 15, 25, 75
5. 2, 4, 31, 62, 124
6. 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
7. 13, 169
8. 5, 7, 25, 35, 175
9. 3, 5, 7, 10, 15, 21, 30, 35, 70, 105, 210
II. Find the prime factors of following numbers.
1. 27
2. 77
3.40
4. 63
5. 143
6. 75
7. 100
8. 185
9. 196
Answer:
II. 1. 3
2. 7, 11
3. 2, 5
4. 3, 7
5. 11, 13
6. 3, 5
7. 2, 5
8. 5, 37
9. 2, 7
III. Find the first six multiples of each number (excluding the number itself).
1. 4
2. 8
3. 12
4. 8
5. 15
6. 17
Answer:
III. 1. 8, 12, 16, 20, 24, 28
2. 16, 24, 32, 40, 48, 56
3. 24, 36, 48, 60, 72, 84
4. 16, 24, 32, 40, 48, 56
5. 30, 45, 60, 75, 90, 105
6. 34, 51, 68, 85, 102, 119
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