Question

What is the prime factorization of 14641?

Answer 1

The prime factorization of 14,641 is 11*11*11*11.

Explanation:

Prime factorization is the finding of the prime factors of a certain number by rigorous division that is the number is divided multiple times by prime factors to ultimately getting the quotient as 1, that is the number is completely factorized and the divisors for each step of the rigorous division is considered as the prime factors of the number to be factorized.

14641 when divided by 11, divides the number completely giving the remainder 0 and the quotient as 1331. Now, the next step is to divide the quotient again by 11. This gives 121. When 121 is divided by 11 again, the remainder found out is 0 and the quotient is 11. Finally, when 11 is divided by 11, we get 1 as the quotient and that gives us the final set of prime factors of the number 14641.

Hence, the prime factorization of 14,641 is 11*11*11*11

Answer 2

`\sf 14641 = 11 * 11 * 11 * 11`

Explanation:

The prime factorization of a number is the product of the prime numbers that divide it.

In order to find the prime factorization of 14641, we can use the following steps:

1. Start by dividing 14641 by the smallest prime number, 2.
2. If 14641 is divisible by 2, then write 2 as a factor of 14641 and divide 14641 by 2.
3. Repeat steps 1 and 2 with the next smallest prime number, 3.
4. Continue repeating steps 1 and 2 until 14641 is no longer divisible by any prime number.
5. The prime factorization of 14641 is the product of all of the prime numbers that we found in steps 1-4.

The prime factorization of 14641 is:

`\sf 14641 = 11 * 1331 = 11 * 11 * 121 = 11 * 11 * 11 * 11`

Therefore, the prime factorization of 14641 is:

`\sf 14641 = 11 * 11 * 11 * 11`