# What is the factorial of hundred

What is the factorial of 100?

Question- 100! = 2^K1 × 3^K2 × 5^K3 × 7^K4× – – –

Answer :- Find = K1, K2, K3, K4, – – –

100! = 100 × 99 × 98 × 97 × 96 × – – – × 3 × 2 × 1

= (100 × 98 × 96 × 94 × – – – × 6 × 4× 2) × (99 × 97 × 95 × – – – × 3 × 1)

= 2^50 ( 50 × 49 × 48 × 47× – – – × 3 × 2 × 1) × ODD Number

= 2^50 (50 × 48 × 46 × 44 × – – – × 3 × 2 × 1) × ODD Number

= 2^50 × 2^25 ( 25 ×24 × 23 × 22 × – – – × 3 × 2 × 1) × ODD NUMBER

= 2^50 × 2^25 (24 × 22 × 20 ×v18 × – – – × 4 × 2) × ODD NUMBER

= 2^50 × 2^25 × 2^12 ( 12 × 11× 10 × – – – × 3 × 2× 1) × ODD NUMBER

= 2^50 × 2^25 × 2^12 ( 12 × 10 × 8 × 6 × 4 × 2) × ODD NUMBER

= 2^50 × 2^25 × 2^12 × 2^6 ( 6 × 5 × 4 × 3 × 2 × 1) ODD NUMBER

= 2^50 × 2^25 × 2^12 × 2^6 ( 6 × 4 × 2) × ODD NUMBER

= 2^50 × 2^25 × 2^12 × 2^6 × 2^3 ( 3 × 2 × 1) × ODD NUMBER

= 2^50 × 2^25 × 2^12 × 2^6 × 2^3 × 2^1 × ODD NUMBER

= 50 + 25 + 12 + 6 + 3 + 1

= 97

## What is the factorial of hundred

100! = ( Multiple of 3) or (Non Multiple of 3)

Exponent of 5 = 100/5

= 20

= 20/5

= 4

= 20 + 4

= 24

OR

### Question – What is the factorial of 100

Answer: The aproximate value of 100! is 9.3326215443944E+157. The number of trailing zeros in 100! is 24. This is the factorial of hundred (factorial of 100!)