Question

the number of even divisors of 100 will be

Answer 1

Hey there!

100 = 25 * 4 = 2² * 5²

We know that,

For n = $p_{1}^{n_{1}}* p_{2}^{n_{2}} * . . . . . . . . . . . p_{k}^{n_{k}}$

d(N)=$(n_{1} + 1 ) (n_{2} + 1 ) (n_{3} + 1 )............... (n_{k} + 1 )$

So here,
p1 = 2 , n1 = 2
p2 = 5 , n2 = 2 .

So,
d(100) = (2+1)(2+1) = 3 * 3 = 9 .

Number of odd divisors = (2+1) = 3 .

Therefore, Number of even divisors = 9 - 3 = 6 .

Here, d(N) means the total number of divisors of N.

Removing the power of 2 from calculating of d(N) , We get odd divisors

Answer 2

Number of even divisors of 100 = 6

Step-by-step explanation:

To find the number of even divisors of 100.

Let us first write the divisors of 100.

Divisors of 100 = 1, 2, 4, 5, 10, 20, 25, 50 and 100.

In the above divisors, write the even divisors.

Even divisors of 100 = 2, 4, 10, 20, 50 and 100.

Number of even divisors = 6

Therefore number of even divisors of 100 is 6.

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