Answer :
To find the common divisors and greatest common divisor (GCD) for the numbers 108, 324, and 516, let’s break it down step-by-step:
1. List all divisors for each number:
- Divisors of 108:
- [tex]\(1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108\)[/tex]
- Divisors of 324:
- [tex]\(1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324\)[/tex]
- Divisors of 516:
- [tex]\(1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516\)[/tex]
2. Identify the common divisors:
- To find the common divisors, we need to find numbers that are in all three lists.
- Common divisors of 108, 324, and 516:
- [tex]\(1, 2, 3, 4, 6, 12\)[/tex]
3. Determine the greatest common divisor (GCD):
- The greatest common divisor is the largest number in the list of common divisors.
- Among the common divisors [tex]\(1, 2, 3, 4, 6, 12\)[/tex], the largest number is [tex]\(12\)[/tex].
So, the common divisors of 108, 324, and 516 are [tex]\(1, 2, 3, 4, 6, 12\)[/tex] and the greatest common divisor (GCD) is [tex]\(12\)[/tex].
1. List all divisors for each number:
- Divisors of 108:
- [tex]\(1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108\)[/tex]
- Divisors of 324:
- [tex]\(1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324\)[/tex]
- Divisors of 516:
- [tex]\(1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516\)[/tex]
2. Identify the common divisors:
- To find the common divisors, we need to find numbers that are in all three lists.
- Common divisors of 108, 324, and 516:
- [tex]\(1, 2, 3, 4, 6, 12\)[/tex]
3. Determine the greatest common divisor (GCD):
- The greatest common divisor is the largest number in the list of common divisors.
- Among the common divisors [tex]\(1, 2, 3, 4, 6, 12\)[/tex], the largest number is [tex]\(12\)[/tex].
So, the common divisors of 108, 324, and 516 are [tex]\(1, 2, 3, 4, 6, 12\)[/tex] and the greatest common divisor (GCD) is [tex]\(12\)[/tex].
