Answer to Question #239632 in Combinatorics | Number Theory for jerico

Question

Find the prime factorization of the integers 1234, 10140, and 36000

Answer 1

Consider the following integers:

1234,10140, and 36000

The objective is to find the prime factorization of the above-mentioned integers.

Recall that a positive integer can be uniquely expressed as the product of prime numbers.

The prime factorization of the given number is as follows:

$1234= 2\times617 \\ 10140= 2\times2\times3\times5\times13\times13=2^2\times3\times5\times13^2 \\ 36000=2\times2\times2\times2\times2\times3\times3\times5\times5\times5=2^5\times3^2\times5^3$

Therefore, the prime factorization of the given integers are

$1234= 2\times617 \\ 10140=2^2\times3\times5\times13^2 \\ 36000=2^5\times3^2\times5^3$