Find the prime factorization of the number
-32,625
A) $5 ^ { 4 } \cdot 29$
B) $3 ^ { 4 } \cdot 29$
C) $3 ^ { 2 } \cdot 5 ^ { 3 } \cdot 29$
D) $3 ^ { 3 } \cdot 5 ^ { 2 } \cdot 29$

Question

Find the prime factorization of the number
-32,625 
A) $5 ^ { 4 } \cdot 29$
B) $3 ^ { 4 } \cdot 29$
C) $3 ^ { 2 } \cdot 5 ^ { 3 } \cdot 29$
D) $3 ^ { 3 } \cdot 5 ^ { 2 } \cdot 29$

Quizplus · Accepted Answer

The prime factorization of 32,625 can be found by dividing the number by its smallest prime factor and continuing the process with the quotient until only prime numbers are left. Starting with 32,625, we see that it is divisible by 5 (since it ends in 5), giving us $5 \times 6525$. Continuing to factor 6525, we find it is also divisible by 5, giving us $5^2 \times 1305$. Further dividing 1305 by 5 gives $5^3 \times 261$. Finally, 261 can be divided by 3 twice to get $3^2 \times 29$. Since 29 is a prime number, we cannot factor it further. Thus, the prime factorization of 32,625 is $3^2 \cdot 5^3 \cdot 29$, which matches option C.

Find the Prime Factorization of the Number -32,625 A) 54⋅295 ^ { 4 } \cdot 2954⋅29

Find the Prime Factorization of the Number
-32,625
A) $5 ^ { 4 } \cdot 29$