Chapter : Real Numbers
Finding Prime factor by Factor Tree division Method
Example: Find the prime factors of : (i) 540 (ii) 21252 (iii) 8232.
Solution:
(i) 
5 is a prime number and so cannot be further divided by any prime number
∴ 540 = 2 × 2 × 3 × 3 × 3 × 5 = 22 × 33 ×5
(ii) 
∴ 21252 = 2 × 2 × 3 × 7 × 11 × 23
= 22 × 3 × 11 × 7 × 23.
(iii) 
∴ 8232 = 2 × 2 × 2 × 3 × 7 × 7 × 7 = 23 × 3 × 73.
Example : Find the missing numbers a, b and c in the following factorisation:
Can you find the number on top without finding the other ?
Solution :
c = 17 × 2 = 34
b = c × 2 = 34 × 2 = 68 and
a = b × 2 = 68 × 2 = 136
i.e., a = 136, b = 68 and c = 34. (Ans)
Yes, we can find the number on top without finding the others.
Reason: The given numbers 2, 2, 2 and 17 are the only prime factors of the number on top and so the number on top = 2 × 2 × 2 × 17 = 136
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