Page 49 - Maths Skill - 6

Prime Time 47

5. Write the smallest 6-digit number and express it as a product of prime factors.

6. Write the largest 4-digit number and find its prime factors.

COMMON FACTORS AND COMMON MULTIPLES

Common Factors
Factors that are common to two or more numbers are said to be common factors.
For example; Factors of 15 are 1, 3, 5, 15
Factors of 20 are 1, 2, 4, 5, 10 and 20

So, common factors of 15 and 20 are 1 and 5.

Common Multiples
Multiples that are common to two or more numbers are said to be common multiples
For example; Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, ............
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, ............

So, common multiples of 3 and 4 are 12, 24

Let’s Attempt

Example 1: Find the first three common multiples of 3, 5 and 15.
Solution: Multiples of 3 ⇒ 3, 6, 9, 12, 15 , 18, 21, 24, 27, 30 , 33, 36, 39, 42, 45 , 48, ....

Multiples of 5 ⇒ 5, 10, 15 , 20, 25, 30 , 35, 40, 45 , 50, ....

Multiples of 15 ⇒ 15 , 30 , 45 , 60, ....

The common multiples are 15, 30, 45, so on.

Example 2: Write the common factors of 8, 20, 36.
Solution: Factors of 8 ⇒ 1, 2, 4, 8
Factors of 20 ⇒ 1, 2, 4, 5, 10, 20
Factors of 36 ⇒ 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors of 8, 20 and 36 are 1, 2 and 4.

Example 3: Find the common factors of 36, 84.
Solution: Factors of 36 ⇒ 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 84 ⇒ 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The common factors of 36 and 84 are 1, 2, 3, 4, 6, 12.

Example 4: Find the common factors of 136, 64, 24, 16.

Solution: Factors of 136 ⇒ 1, 2, 4, 8, 17, 34, 68, 136
Factors of 64 ⇒ 1, 2, 4, 8, 16, 32, 64
Factors of 24 ⇒ 1, 2, 3, 4, 6, 8, 12, 24
Factors of 16 ⇒ 1, 2, 4, 8, 16

The common factors of 136, 64, 24, 16 are 1, 2, 4, 8.