Express 315 as the product of prime numbers?

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Answer

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2.2 cancel 1.4

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Answer

According to the article, 315 can be expressed as the product of prime numbers by following these steps:

Continuously divide the number by the smallest prime number (2) until it is no longer divisible by 2.
If the number is still not a prime number, continue dividing it by the next smallest prime number (3) and so on.
Repeat steps 1 and 2 until you are left with only prime numbers.

The article also provides a detailed solution, which likely involves dividing 315 by prime numbers until you reach the prime factorization.

Let me know if you'd like me to find the prime factorization of 315 for you.

Answer

Prime Factorization of 315

Prime factorization is the process of breaking down a number into its prime factors. To express 315 as the product of prime numbers, we need to find its prime factors.

Step 1: Finding the Smallest Prime Factor

The smallest prime number is 2, but 315 is not divisible by 2. Therefore, we move on to the next prime number, which is 3.

Step 2: Dividing by the Smallest Prime Factor

Divide 315 by 3:

315 ÷ 3 = 105

Step 3: Repeat the Process

We continue the process with the quotient obtained from the previous step, which is 105.

Step 4: Finding the Next Smallest Prime Factor

The next prime number after 3 is 5. We check if 105 is divisible by 5.

Step 5: Dividing by the Next Smallest Prime Factor

Divide 105 by 5:

105 ÷ 5 = 21

Step 6: Repeat the Process

We continue the process with the quotient obtained from the previous step, which is 21.

Step 7: Finding the Next Smallest Prime Factor

The next prime number after 5 is 7. We check if 21 is divisible by 7.

Step 8: Dividing by the Next Smallest Prime Factor

Divide 21 by 7:

21 ÷ 7 = 3

Step 9: Repeat the Process

We continue the process with the quotient obtained from the previous step, which is 3.

Step 10: Finding the Next Smallest Prime Factor

The next prime number after 7 is 11. We check if 3 is divisible by 11.

Step 11: No More Prime Factors

Since 3 is not divisible by 11, we have found all the prime factors of 315.

Prime Factorization of 315

Therefore, the prime factorization of 315 is:

315 = 3 × 3 × 5 × 7

In Summary

To express 315 as the product of prime numbers, we divided it by the smallest prime factors successively until we could no longer divide. The prime factorization of 315 is given by multiplying its prime factors together: 3 × 3 × 5 × 7.

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