Question

Find the number of odd factors of 2400?​

Answer 1

Given : Find the number of odd factors of 2400

To find : No. of odd factors

Solution :

Factors of a number are numbers which leave remainder 0 on dividing the number with its factor.

Factors of a number can be found using prime factorization method.

Odd numbers are numbers which leaves remainder 1 on dividing by 2.

Factors of 2400 can be represented as :

2400 = 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5

Here, the factors of 2400 are 2, 3 and 5.

No. of odd factors are 3 in which 3 is once and 5 is twice.

Answer 2

There are 6 odd factors of 2400  ( 6 odd Factors are : 1 , 3 , 5 , 15 , 25 , 75)

Given:

• Number 2400

To Find:

• Number of odd factors

Solution:

• "Prime Factorization is finding prime numbers/factors which when multiplied together results in the original number"
• Prime number is a natural number which has only two factors one and number itself.  (e.g. , 2 , 3 , 5 , 7 .... )

Step 1:

Prime factorize 2400

2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5

2400 = 2⁵ x 3¹ x 5²

Step 2:

Odd factor will not have 2 or multiple of 2 as factor Hence ignore 2⁵

Left factor is   3¹ x 5²

Step 3:

Calculate total number of factors using factors of  xᵃ * yᵇ  are  (a + 1)(b + 1)  where x and y are prime

= (1 + 1)(2 + 1)

= (2)(3)

= 6

Hence There are 6 odd factors of 2400

6 Factors are:

1 , 3 , 5 , 15 , 25 and 75