Question

# Give the prime factorization of the number. Use exponential form. 7875

Polynomial factorization
Give the prime factorization of the number. Use exponential form.
7875

2021-06-05

Step 1
Consider the given number 7875.
Step 2
Obtain the prime factorization of the number 7875 as follows.
$$7875 = 3\times 2625\ \ \ [3\times 2625 = 7875]$$
$$=3\times 3\times 875\ \ \ [3\times 875 = 2625]$$
$$=3\times 3\times 5\times 175\ \ \ [5\times 175=875]$$
$$=3\times 3\times 5\times 5\times 35\ \ \ [5\times 35=175]$$
$$=3\times 3\times 5\times 5\times 5\times 7\ \ \ [5\times 7 = 35]$$
$$=3^{2}\times5^{3}\times7$$
Thus, the prime factorization of the number 7875 is $$3^{2}\times5^{3}\times7$$.