Find the prime factorization of 10!.

jeliceg2

jeliceg2

Answered question

2021-12-05

Find the prime factorization of 10!.

Answer & Explanation

Sevensis1977

Sevensis1977

Beginner2021-12-06Added 15 answers

By the definition of factorial:
10!=10*9*8*7*6*5*4*3*2*1
=10*9*8*7*6*5*4*3*2
2, 3,5 and 7 are primes. Let us determine the prime factorization of all other factors.
To determine the prime factorization, we divide the given integer by successive primes. If the remainder is zero, then the prime is part of the factorization and we continue the prime factorization with the quotient.
10=2*5
9=3*3
8=2*2*2
6=2*3
4=2*2
We use these prime factorization in the above found product:
10!=10*9*8*7*6*5*4*3*2
=(2*5)*(3*3)*(2*2*2)*7*(2*3)*5*(2*2)*3*2
Finally combine like terms:
102834527
Result:
2834527

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