GCF of 8 and 12
GCF of 8 and 12
To find the Greatest Common Factor (GCF) of 8 and 12, use one of three methods: prime factorization, long division, or listing common factors. By prime factorization, 8 is 2³ and 12 is 2²× 3 , with the common factor being 2², which is 4. Using the long division method, dividing 12 by 8 gives a remainder of 4, and dividing 8 by 4 leaves a remainder of 0, making 4 the GCF. Listing factors, 8’s factors are 1, 2, 4, 8, and 12’s factors are 1, 2, 3, 4, 6, 12; the greatest common factor is 4. Thus, the GCF of 8 and 12 is 4.
GCF of 8 and 12
GCF of 8 and 12 is 4.
The GCF of 8 and 12 is 4, found by prime factorization (common factor 2²), long division (remainder zero at 4), or listing common factors (1, 2, 4).
Methods to Find GCF of 8 and 12
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 8 and 12 by Prime Factorization Method
Prime factorize each number:
- Prime factors of 8: 8 = 2 × 2 × 2³
- Prime factors of 12: 12 = 2 × 2 × 3 =2²×3
Identify the common prime factors:
- The common prime factor is 2.
- The smallest power of the common factor 2 in both factorizations is 2².
Multiply the common prime factors with the smallest exponents:
GCF = 2² = 4
GCF of 8 and 12 by Long Division Method.
Divide the larger number by the smaller number:
- Larger number: 12
- Smaller number: 8
12 ÷ 8 = 1 (quotient), remainder = 12 − (8×1) = 4
Replace the larger number with the smaller number and the smaller number with the remainder:
- New larger number: 8
- New smaller number: 4
Divide the new larger number by the new smaller number:
8 ÷ 4 = 2 (quotient), remainder = 8 − (4×2) = 0
Repeat the process until the remainder is 0:
- In the second step, the remainder is 0, which means the process stops here.
The divisor at this step is the GCF:
The divisors at the last step before the remainder became 0 is 4.
GCF of 8 and 12 by Listing Common Factors
List the factors of each number:
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Identify the common factors:
The common factors of 8 and 12 are: 1, 2, 4
Determine the greatest common factor:
Among the common factors, the largest one is 4.
What is the GCF of 8 and 12?
The Greatest Common Factor (GCF) of 8 and 12 is 4.
Can the GCF be larger than the smallest number?
No, the GCF cannot be larger than the smallest of the given numbers.
What is the relationship between GCF and LCM?
The product of the GCF and the Least Common Multiple (LCM) of two numbers equals the product of the numbers themselves.
How can understanding GCF benefit students in math?
Understanding GCF helps students simplify fractions, solve problems involving divisors, and enhance their number theory skills.
What is the GCF of 8 and 12 used for in real life?
The GCF can be used for reducing fractions, dividing items into equal groups, and solving problems in finance, engineering, and computer science.
Can the GCF of two numbers be one of the numbers?
Yes, if one number is a multiple of the other, the GCF is the smaller number. For example, the GCF of 4 and 8 is 4.
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