Find the GCF of the numbers using an appropriate method.
84 and 126
Find the prime factorization of the number, and write it in exponent form.
198
1) Find the prime factors of each respective number.
84 = 2 x 2 x 3 x 7
126 = 2 x 3 x 3 x 7
Multiply the factors both numbers have in common. In this case multiply 2, 3 and 7.
Therefore, the answer is: 42
2) Again, we will find the prime numbers that go into 198. First divide by the smallest prime number that you can think of that goes easily into 198. I generally start with 2.
198/2 = 99
99/3 = 33
33/3 = 11
Therefore, your answers are 3^2, 2, and 11.
84- 2^2 3 7
126- 2 3^2 7
GCF= 2*3*7= 42
198- 2 3^2 11
To find the greatest common factor (GCF) of two numbers, you can use the method of prime factorization. Here's how you can find the GCF of 84 and 126:
Step 1: Determine the prime factorization of each number.
For 84:
84 can be divided by 2, resulting in 42.
42 can be divided by 2, resulting in 21.
21 can be divided by 3, resulting in 7.
Therefore, the prime factorization of 84 is 2 * 2 * 3 * 7.
For 126:
126 can be divided by 2, resulting in 63.
63 can be divided by 3, resulting in 21.
21 can be divided by 3, resulting in 7.
Therefore, the prime factorization of 126 is 2 * 3 * 3 * 7.
Step 2: Identify the common factors.
When comparing the prime factorizations of both numbers, we can see that the common factors are 2, 3, and 7.
Step 3: Multiply the common factors.
To find the GCF, we multiply the common factors together:
GCF = 2 * 3 * 7 = 42.
Therefore, the GCF of 84 and 126 is 42.
Now, let's find the prime factorization of 198:
Step 1: Divide the number by the smallest prime number possible, which is 2.
198 ÷ 2 = 99
Step 2: Repeat the process until the quotient is a prime number.
99 ÷ 3 = 33
33 ÷ 3 = 11
Step 3: The prime factorization of 198 is 2 * 3 * 3 * 11, or written in exponent form as 2^1 * 3^2 * 11^1.