How can you simplify the following fraction using prime factorization?:
#832/644#

Question

Zoe Adams · Accepted Answer

#832/644=208/161# Prime factors of #832# are #832=2xx2xx2xx2xx2xx2xx13# and prime factors of #644# are #644=2xx2xx161# Hence #832/644=(2xx2xx2xx2xx2xx2xx13)/(2xx2xx161)# = #(cancel(2xx2)xx2xx2xx2xx2xx13)/(cancel(2xx2)xx161)# = #(2xx2xx2xx2xx13)/161# = #208/161#

Levi Adams · Answer

undefined To simplify the fraction $ \frac{832}{644} $ using prime factorization:

1. Find the prime factorization of both the numerator and the denominator.
2. Cancel out common prime factors from the numerator and denominator.
3. Multiply the remaining factors to obtain the simplified fraction.

Prime factorization of 832:
$$ 832 = 2 \times 2 \times 2 \times 2 \times 13 = 2^4 \times 13 $$

Prime factorization of 644:
$$ 644 = 2 \times 2 \times 7 \times 23 = 2^2 \times 7 \times 23 $$

Cancel out common prime factors:
$$ \frac{832}{644} = \frac{2^4 \times 13}{2^2 \times 7 \times 23} $$

$$ = \frac{2 \times 2 \times 2 \times 2 \times 13}{2 \times 2 \times 7 \times 23} $$

$$ = \frac{2 \times 13}{7 \times 23} $$

$$ = \frac{26}{161} $$

Therefore, the simplified form of $ \frac{832}{644} $ using prime factorization is $ \frac{26}{161} $.

How can you simplify the following fraction using prime factorization?: #832/644#