Write the number 117 as a product of prime factors. 117 = \boxed{ }
The Correct Answer and Explanation is:
To express 117 as a product of prime factors, we begin by performing a prime factorization.
- Check divisibility by 2:
117 is odd, so it is not divisible by 2. - Check divisibility by 3:
To check divisibility by 3, we sum the digits of 117:
1+1+7=91 + 1 + 7 = 91+1+7=9.
Since 9 is divisible by 3, 117 is divisible by 3.
Dividing 117 by 3 gives: 117÷3=39117 \div 3 = 39117÷3=39 - Factor 39:
Now, we factor 39. Again, we check for divisibility by 3.
Summing the digits of 39:
3+9=123 + 9 = 123+9=12, and since 12 is divisible by 3, 39 is divisible by 3.
Dividing 39 by 3 gives: 39÷3=1339 \div 3 = 1339÷3=13 - Prime factorization of 13:
The number 13 is a prime number, meaning it cannot be divided further.
Now we can express 117 as the product of prime factors: 117=3×3×13117 = 3 \times 3 \times 13117=3×3×13
or more simply: 117=32×13117 = 3^2 \times 13117=32×13
Thus, the prime factorization of 117 is 32×13\boxed{3^2 \times 13}32×13.
Explanation:
Prime factorization is the process of breaking down a number into the prime numbers that multiply together to give the original number. We start with the smallest prime, 2, and check divisibility. If a number is divisible by 2, we continue dividing by 2 until it’s no longer divisible. If it’s not divisible by 2, we check the next smallest prime, which is 3, and repeat the process. We continue this until all factors are prime numbers. In the case of 117, the prime factors are 3 and 13, giving the final result of 32×133^2 \times 1332×13.
