prime factorization of 693
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.
To find the prime factorization of 693, we need to determine its prime factors.
First, let's find the smallest prime number that divides 693. The smallest prime number is 2, but 2 does not divide 693 evenly.
Next, let's try the next prime number, which is 3. When we divide 693 by 3, we get 231 with no remainder.
Now, let's continue factoring 231. We repeat the process by finding the smallest prime number that divides it.
Again, the smallest prime number is 2, but 2 does not divide 231 evenly.
Next, let's try the next prime number, which is 3. When we divide 231 by 3, we get 77 with no remainder.
Now, we have 77 left. Let's continue factoring it.
The smallest prime number that divides 77 is 7. When we divide 77 by 7, we get 11 with no remainder.
Now, we have 11 left. Since 11 is a prime number, we cannot further factorize it.
To summarize, the prime factorization of 693 is: 3 × 3 × 7 × 11.
To find the prime factorization of 693, we need to determine the prime numbers that divide 693 evenly. Here's how you can do it:
1. Begin by dividing 693 by the smallest prime number, which is 2.
- Since 693 is an odd number (not divisible by 2), we move on to the next prime number.
2. Divide 693 by 3.
- 693 ÷ 3 = 231
- Since 231 is still not divisible by 3, we continue to the next prime number.
3. Divide 693 by 5.
- 693 ÷ 5 = 138.6
- Since 138.6 is not a whole number, it means that 693 is not divisible by 5.
4. Divide 693 by 7.
- 693 ÷ 7 = 99
- 99 is divisible by 7, so we have found one prime factor, which is 7.
5. Divide 99 by 7.
- 99 ÷ 7 = 14.14
- 14.14 is not a whole number, so 99 is not divisible by 7 again.
6. Finally, divide 99 by 11.
- 99 ÷ 11 = 9
- 9 is divisible by 11, so we have found another prime factor, which is 11.
Since we have found the prime factors 7 and 11, we can conclude that the prime factorization of 693 is: 7 x 11.