Home
Class 11
MATHS
Find the exponent of 3 in 100!...

Find the exponent of 3 in 100!

Text Solution

Verified by Experts

In terms of prime factors 100! Can be written as `2^(a)*3^(b)*5^(c)*7^(d)`
Now, `b=E_(3)(100!)`
`=[(100)/(3)]+[(100)/(3^(4))]+[(100)/(3^(3))]+[(100)/(3^(4))]` + . . .
`=33+11+3+1+0+ . . .=48`
Hence, exponent of 3 is 48.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the exponent of 80 in 200!.

Find the exponent of 80 in 200!.

Particles of masses 1g, 2g, 3g ….100g are kept at the marks 1cm, 2cm, 3cm …., 100 cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

The sum of the exponents of the prime factors in the prime factorisation of 504 is ……………….

The sum of the exponents of the prime factors in the prime factorization of 1729 is

The sum of the exponents of the prime factors in the prime factorization of 1729 is :

Find the number of ways in which 3 distinct numbers can be selected from the set {3^(1),3^(2),3^(3),..,3^(100),3^(101)} so that they form a G.P.