Page 85 - ICSE Math 4

This method is used when it becomes diffi cult to make factor trees for larger numbers. We
start with the smallest prime number that can divide the given number exactly. We keep
on dividing the number ll we get a prime number or 1 as the quo ent. Then we mul ply
all the prime numbers to obtain the given number.

Example 10: Find the prime factors of the following numbers using the prime factoriza on
method.

(a) 84 (b) 384
Solu on: (a) 84 (b) 384

2 84 (84 ÷ 2 = 42) 2 384 (384 ÷ 2 = 192)
2 42 (42 ÷ 2 = 21) 2 192 (192 ÷ 2 = 96)
3 21 (21 ÷ 3 = 7) 2 96 (96 ÷ 2 = 48)

7 7 (7 ÷ 7 = 1) 2 48 (48 ÷ 2 = 24)
1 (Quo ent) 2 24 (24 ÷ 2 = 12)
2 12 (12 ÷ 2 = 6)
2 6 (6 ÷ 2 = 3)
3 3 (3 ÷ 3 = 1)
1 (Quo ent)
So, the prime factors of 84 are So, the prime factors of 384 are

2 × 2 × 3 × 7. 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3.

Exercise 7.3

1. Fill in the blanks.
(a) __________ and ___________ are the prime numbers having a diff erence of 1.

(b) ___________ is the smallest composite number.

(c) 2 is the only ___________ prime number.

(d) ___________ and ___________ are neither prime nor composite numbers.
(e) The two prime numbers less than 7 and having a diff erence of 3 are __________
and __________.

(f) Each prime number has only ___________ factors.

(g) There are ___________ prime numbers between 1 and 100.
(h) Two consecu ve prime numbers are ___________ and ___________.

(i) ___________ is the method of breaking a number into its factors, which when
mul plied together gives the original number.

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