Question

The H.C.F of the numbers 25, 75, and 100 is
$
  {\text{a}}{\text{. 15}} \\
  {\text{b}}{\text{. 25}} \\
  {\text{c}}{\text{. 5}} \\
  {\text{d}}{\text{. 100}} \\
$

Answer 1

Hint – H.C.F of the numbers is calculated by multiplying all the common factors so, use this property to reach the answer.

Given numbers are 25, 75, and 100
As we know that the highest common factor (H.C.F) is calculated by multiplying all the common factors of the given numbers.
So first factories the numbers,
Therefore the factors of 25 are,
$25 = 5 \times 5$
The factors of 75 are,
$75 = 5 \times 5 \times 3$
The factors of 100 are,
$100 = 5 \times 5 \times 4$
Now, as we see that the common factors of above numbers are $5 \times 5$.
So the required H.C.F of the given numbers is $5 \times 5 = 25$.
So, H.C.F of 25, 75 and 100 is 25
Hence option (b) is correct.

Note – In such types of questions first factories all the given numbers then find out all the common factors of the given numbers then multiply these common factors which is the required H.C.F of the given numbers.