Page 60 - ICSE Math 6

5. Find all common factors of 12 and 20. Also, find the first five common multiples of their common
factors.
6. If the first three common multiples of two numbers are 14, 28 and 42, find their next three common
multiples.

Prime Factorization
The fundamental theorem of Arithmetic states that every composite
number can be factorized into prime factors in a unique way. Consider Maths Info
the composite number 40. We can write 40 as 8 × 5. As 8 is again a A factor which is also a prime
composite number we can write it as 2 × 2 × 2. Hence, 40 = 2 × 2 × 2 number is known as a prime
× 5. Alternatively, we can write 40 as 4 × 10. Now 4 can be written as factor of the given number.
2 × 2 and 10 as 2 × 5, hence, 40 = 2 × 2 × 2 × 5. In both the cases, we obtain the same factorization
2 × 2 × 2 × 5. In this factorization, the factors 2 and 5 are prime numbers. This process of expressing
a number as a product of prime factors is called prime factorization.

A factor tree is a diagram that shows all the factors of a number.

Example 16: Complete the following factor trees for 80.
(a) (b)

80 80

40 ? 10
8

20 ? ? ?
?
4

? 4
2 ?

2 ?

Solution: (a) (b)
80 80

40 2 10 8

20 2 2 5 2
4

5 4 2 2

2 2

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