Write the prime factorization. See Examples 4 through 6.ExampleExample 4 Write the prime f...

Write the prime factorization. See Examples 4 through 6.

Example

Example 4 Write the prime factorization of 45.

Solution: We can begin by writing 45 as the product of two numbers, say 9 and 5.

45 = 9·5

The number 5 is prime, but 9 Is not. So we write 9 as 3·3.

Each factor is now a prime number, so the prime factorization of 45 is 3·3·5.

Example 5 Write the prime factorization of 80.

Solution: We first write 80 as a product of two numbers. We continue this process until all factors are prime.

All factors are now prime, so the prime factorization of 80 is 2·2·2·2·5.

Example 6 Write the prime factorization of 252.

Solution: Since the ones digit of 252 is 2, we know that 252 is divisible by 2.

126 is divisible by 2 also.

63 is not divisible by 2 but is divisible by 3. We divide 63 by 3 and continue in this same manner until the quotient is a prime number.

The prime factorization of 252 is 2·2·3·3·7.

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