how can i find the GCF of a pair of numbers ? (ie 11 18, 8 6)
To find the greatest common factor (GCF) of a pair of numbers, such as 11 and 18 or 8 and 6, you can use a method called prime factorization or use the euclidean algorithm.
Let's start with the first pair of numbers, 11 and 18.
Method 1: Prime Factorization
1. Begin by finding the prime factors of both numbers.
- For 11, since it is a prime number, its only prime factor is 11.
- For 18, you can break it down into prime factors: 2 × 3 × 3.
2. Identify the common prime factors between the two numbers.
- The only common prime factor between 11 and 18 is 3.
3. Multiply the common prime factors together.
- In this case, the GCF of 11 and 18 is 3.
Method 2: Euclidean Algorithm
1. Divide the larger number by the smaller number.
- For example, you would divide 18 by 11.
2. Take the remainder of the division and divide it by the previous divisor (11 in this case).
- Continuing with the example, you would divide the remainder of 18 divided by 11, which is 7, by 11.
3. Repeat this process until you get a remainder of 0.
- Continuing the example, you would divide 11 by 7, which gives you a remainder of 4. Then divide 7 by 4, which gives you a remainder of 3. Finally, divide 4 by 3, which gives you a remainder of 1.
4. The divisor at this step is the GCF of the two numbers.
- In this case, the greatest common factor (GCF) of 11 and 18 is 1.
Now let's move on to the second pair of numbers, 8 and 6.
Method 1: Prime Factorization
1. Find the prime factors of both numbers.
- For 8, its prime factorization is 2 × 2 × 2.
- For 6, its prime factorization is 2 × 3.
2. Identify the common prime factors.
- In this case, the common prime factor between 8 and 6 is 2.
3. Multiply the common prime factors together.
- The GCF of 8 and 6 is 2.
Method 2: Euclidean Algorithm
1. Divide the larger number by the smaller number.
- Divide 8 by 6.
2. Take the remainder and divide it by the previous divisor.
- Divide the remainder of 8 divided by 6, which is 2, by 6.
3. Keep repeating this process until you reach a remainder of 0.
- Divide 6 by 2, which gives you a remainder of 0.
4. The divisor at this step is the GCF of the two numbers.
- In this case, the GCF of 8 and 6 is 2.
By using either the prime factorization method or the Euclidean algorithm, you can find the greatest common factor (GCF) between any pair of numbers.