Math

QuestionFind the prime factorization of 676, using exponents for repeated factors.

Studdy Solution

STEP 1

Assumptions1. The number is676. We need to find the prime factorization of this number3. Repeated factors should be written using exponents

STEP 2

Prime factorization is the process of finding the prime numbers that multiply together to make a certain number. We start by dividing the number by the smallest prime number, which is2.
676÷2=338676 \div2 =338

STEP 3

The result is338, which is not a prime number. So, we continue the process by dividing338 by2.
338÷2=169338 \div2 =169

STEP 4

The result is169, which is not a prime number. We can't divide it by2, so we try the next prime number, which is3. But169 is not divisible by3. So, we try the next prime number, which is. But169 is not divisible by. So, we try the next prime number, which is7. But169 is not divisible by7. So, we try the next prime number, which is11. But169 is not divisible by11. So, we try the next prime number, which is13.
169÷13=13169 \div13 =13

STEP 5

The result is13, which is a prime number. So, we divide13 by13.
13÷13=113 \div13 =1

STEP 6

The result is1, which means we have found all the prime factors of676. They are2,2,13, and13.

STEP 7

Since we have to write repeated factors using exponents, we write2 two times as 222^2 and13 two times as 13213^2.
So, the prime factorization of676 is 22×1322^2 \times13^2.

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