What are the factors of 117? I’ve tried, and I can’t find them.
The Correct Answer and Explanation is:
The factors of 117 are the numbers that divide 117 exactly, leaving no remainder. To find these factors, we start with the smallest number (1) and check each integer to see if it divides 117.
- Start with 1: Every number is divisible by 1, so 1 is a factor of 117.
- Check 2: Since 117 is an odd number, it is not divisible by 2.
- Check 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For 117, the sum of the digits is 1 + 1 + 7 = 9, which is divisible by 3. Therefore, 117 ÷ 3 = 39. So, 3 is a factor, and 39 is also a factor.
- Check 5: Since 117 does not end in 0 or 5, it is not divisible by 5.
- Check 7: Dividing 117 by 7 gives 117 ÷ 7 = 16.71, which is not an integer. So, 7 is not a factor.
- Check 9: Since 39 (a factor of 117) is divisible by 9 (39 ÷ 9 = 4.33), 9 is not a factor either.
- Continue with 13: Dividing 117 by 13 gives 117 ÷ 13 = 9, which is an integer. So, 13 is a factor, and 9 is also a factor.
Therefore, the complete list of factors for 117 is:
1, 3, 9, 13, 39, and 117.
Explanation:
The process for finding the factors involves dividing the number by consecutive integers and checking if the result is an integer (i.e., no remainder). Factors come in pairs: when you divide a number (in this case, 117) by a divisor (such as 3), the quotient (39) is also a factor. Thus, we end up with these pairs of factors: 1 and 117, 3 and 39, 9 and 13.
