Question

which are the numbers between 1 and 100 having exactly three factors

Answer 1

Answer:

The numbers 4, 9, 25, 49 only has 3 factors exactly below 100.

Explanation:

All the prime numbers between 1 and 100 like 3, 5, 11…have exactly two factors, those are 1 and itself i.e.., only two factors.

All the composite numbers like 6,8, 12 …. Have more than 3 factors like for 6( 1, 2, 3, 6)…8(1,2,4,8)…….

So, no composite number has three factors, and prime numbers have two factors.

Let us consider the square of prime numbers which are below 100.

That is 4(2×2) , 9(3×3) , 25(5×5) , 49(7×7)  

Here,  

factors of 4 are 1, 2, 4

factors of 9 are 1, 3, 9

factors of 25 are 1, 5, 25    

factors of 49 are 1, 7, 49

Therefore, the numbers between 1 and 100 with exactly 3 factors are 4, 9, 25, 49.

Answer 2

Answer:

the number which have three factors:

1)4..

2)9..

3)25 ..

4)49