Page 99 - Start Up Mathematics_4

Factor tree method

In factor tree method, we keep breaking down a number into factors till all the factors are
prime numbers. These prime numbers are usually circled. The shape of a factor tree depends
upon how you factorize a number.

Example 3: Write 24 as a product of its prime factors by making a factor tree.
Solution: 24 24 24

4 6 3 8 2 12

2 2 3 2 2 4 3 4

2 2 2 2
So, 24 = 2 × 2 × 2 × 3.

Division method

Sometimes, for bigger numbers it becomes difficult to make factor trees. So we use the
division method.

Start with the smallest prime number that can divide the given number exactly. Keep dividing
by prime numbers till the quotient becomes 1.
Example 4: Write the prime factorization of 96 using the division method.

Solution: 2 96 (96 ÷ 2 = 48)

2 48 (48 ÷ 2 = 24)
2 24 (24 ÷ 2 = 12)

2 12 (12 ÷ 2 = 6)
2 6 (6 ÷ 2 = 3)

3 3 (3 ÷ 3 = 1)
1 (Quotient)

So, 96 = 2 × 2 × 2 × 2 × 2 × 3.
Example 5: Write 84 as a product of its prime factors.

Solution: 2 84

2 42

3 21
7 7

1
So, 84 = 2 × 2 × 3 × 7.

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