Question

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. $3$
• B. $15$
• C. $30$
• D. $75$

Answer 1

Answer: (B), (C)

$30$

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 $125.$

$\Rightarrow 125=5^3$

$\therefore$ The second number is a multiple of $3$ and have 5 as greatest common factor with 125.

From the given options, such numbers are $15,30$

$\to 15=3\times 5\to 30=2\times 3\times 5\to 75=3\times 5\times 5$

To verify this, let's generate the Factor Tree of $15$ and $30.$

15 and 30 satisfy the given conditions.