Two numbers have HCF 4 and LCM 48. If one number is 16, find the other number.

Class 6Playing with NumbersPlaying with Numbers

Step-by-Step Solution

For two numbers a and

b : a \times b

= HCF × LCM. So

16 \times b = 4 \times 48 = 192

, giving

b = 192 \div 16 = 12

Answer: D) 12

Key idea: Factors come in pairs

To find every factor of a number, walk up from 1 and check each whole number — if it divides the number with no remainder, it is a factor. Factors come in **pairs**: if 4 is a factor of 12, so is 12 ÷ 4 = 3. So you only need to check up to the square root of the number to find them all. Factors of 12:

1 \times 12, 2 \times 6, 3 \times 4

— six factors total: 1, 2, 3, 4, 6, 12. Every number has 1 and itself as factors.

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