GCD of two numbers is 5. If one number is 125 and another number is a multiple of 3, find the possible number(s) using Factor Tree.
A
3
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B
15
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C
30
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D
75
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Solution
The correct option is C30 It is given that the GCD of two numbers is 5.
GCD is a greatest common factor of both numbers.
One of the numbers is 125. ⇒125=53
∴ The second number is a multiple of 3 and have 5 as greatest common factor with 125.
From the given options, such numbers are 15,30
→15=3×5→30=2×3×5→75=3×5×5
To verify this, let's generate the Factor Tree of 15 and 30.
15 and 30 satisfy the given conditions.