Question

prime factorization of 693

Answer 1

To find the prime factorization of 693, we need to find the prime numbers that multiply together to obtain 693.

First, we can check if 2 is a factor of 693. Since 693 is an odd number (not divisible by 2), 2 is not a factor of 693.

Next, we can check if 3 is a factor of 693. Adding the digits of 693 (6 + 9 + 3), we get 18. Since 18 is divisible by 3, 693 is also divisible by 3.

Dividing 693 by 3, we get 231.

Now, we need to find the prime factors of 231. Again, we can check if 2 is a factor. Since 231 is an odd number, 2 is not a factor of 231.

Next, we can check if 3 is a factor of 231. Adding the digits of 231 (2 + 3 + 1), we get 6. Since 6 is divisible by 3, 231 is also divisible by 3.

Dividing 231 by 3, we get 77.

Now, we need to find the prime factors of 77. Checking if 2 is a factor, we find that it is not.

Next, we check if 3 is a factor. Since 7 + 7 = 14 is not divisible by 3, 77 is not divisible by 3.

Now, we check if 5 is a factor. Since 77 is not divisible by 5, 77 does not have 5 as a factor.

Since we have not found any more prime factors of 77, we know that 77 itself is a prime number.

Therefore, the prime factorization of 693 is 3 * 3 * 7 * 11.

In exponent form, we can write it as 3^2 * 7 * 11.