Question

Find the largest perfect square factor of 48.

Answer 1

Hint: We have to find the largest perfect square factor of 48. As 48 is an even number, so it will be divisible only by even numbers. Now, point out all even numbers up to 24. Then, search for those even numbers which can divide 48. Now, point out the largest even number up to the number 24 and check that the number is a perfect square. Ignore the numbers which are not perfect squares.

Complete step by step answer:
According to the question, we have the number 48 and we have to find that factor which is the largest perfect square possible.
First of all, we have to find its factors.
The factor of a number is defined as a number which divides the given number and leaves 0 as its remainder.
Here, we need to find factors of 48. It means that we have to find those numbers which divide 48 and leave 0 as the remainder.
We can see that 48 is an even number. So, it is divisible by 2.
Since 48 is an even number so 48 will be divisible only by even numbers except 1.
Now, we have to list all the even numbers up to 24.
The numbers which are even are 2, 4, 6, 8, 10, 12, 14, 18, 20, 22, and 24.
From all the even numbers mentioned above, we can see that the factors of 48 are 1, 2, 4, 6, 8, 12, 16, 24, and 48.
Now, we have to ignore those even numbers which are not perfect squares.
Out of 1, 2, 4, 6, 8, 12, 16, 24, and 48, 2, 6, 8, 12, 24 and 48 is not the perfect square.
Out of 1, 2, 4, 6, 8, 12, 16, 24, and 48, we have 1, 4 and 16 as perfect squares.
We have to find the largest perfect square factor.
16 is greater than 4. So, the largest perfect square factor is 16.

Note: In this question, one can write 4 as answers which is wrong. We have to find the largest possible perfect square factor of 48 and 16 is greater than 4. Hence, 16 is the largest possible perfect square factor of 48.