Find the prime factorization of the number.
-4725
A) $3 ^ { 4 } \cdot 5 \cdot 7$
B) $3 ^ { 3 } \cdot 5 ^ { 3 } \cdot 7$
C) $3 ^ { 3 } \cdot 5 ^ { 2 } \cdot 7$
D) $3 \cdot 5 ^ { 4 } \cdot 7$

Question

Quizplus · Accepted Answer

The prime factorization of 4725 can be found by dividing it by its smallest prime factor and continuing the process with the quotient until we reach 1. Starting with 4725, we divide by 3 (the smallest prime number) to get 1575. Dividing 1575 by 3 again gives 525. Dividing 525 by 3 gives 175. This indicates that 3 is a factor three times, or $3^3$. Continuing, 175 can be divided by 5 to get 35, and then 35 can be divided by 5 again to get 7. Thus, 5 is a factor twice, or $5^2$, and 7 is a factor once. Therefore, the prime factorization of 4725 is $3^3 \cdot 5^2 \cdot 7$.

Find the Prime Factorization of the Number 34⋅5⋅73 ^ { 4 } \cdot 5 \cdot 734⋅5⋅7

Find the Prime Factorization of the Number $3 ^ { 4 } \cdot 5 \cdot 7$