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Chapter 5: Problem 41

Find the prime factorization of each composite number. 3675

Short Answer

Expert verified
The prime factorization of 3675 is \(3 \times 5 \times 5 \times 5 \times 7 \times 7\).

Step by step solution

01

Understanding prime factorization

Prime factorization is finding which prime numbers multiply together to get the original number. A prime number can only be divided by 1 or itself, and it must be a whole number greater than 1.
02

Start with the smallest prime number

The smallest prime number is 2 but 3675 does not divide evenly by 2 as it is an odd number. So, we move on to the next smallest prime number, which is 3. Dividing 3675 by 3 gives 1225.
03

Continue the prime factorization for 1225

The next smallest prime number is not 4 because 4 can be divided by 2 and itself. Hence, 4 is not a prime number. The number 1225 does not divide evenly by the next smallest prime number 3, so we continue with 5. Dividing 1225 by 5 results in 245.
04

Continue the prime factorization for 245

The number 245 divides evenly by 5, resulting in 49.
05

Continue the prime factorization for 49

The number 49 divides evenly by 7, resulting in 7.
06

Finalization

Since 7 is a prime number and cannot be further divided, we stop here. Therefore, combining all the found prime numbers we get the prime factorization of 3675.

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