231 LearnersLast updated on May 26th, 2025
GCF of 8 and 12
The GCF of any two or more numbers is the greatest common factor among the given numbers. In daily life, GCF helps in easy grouping of items and designing arrangements. In this topic, we will learn about the GCF of 8 and 12 and the mistakes and tips related to it.
What is the GCF of 8 and 12
The largest common factor of 8 and 12 is the GCF. Here, the GCF of 8 and 12 is 4. GCF is also called GCD, or the greatest common divisor. The GCF of two numbers is the common factor between the numbers. When two co-primes are considered, the GCF will always be 1.
How to find the GCF of 8 and 12
To solve GCF, children learn different methods. A few well-known methods for solving GCF are as follows -
- Using Listing the Common Factors
- Using Prime Factorization
- Using Division Method
GCF of 8 and 12 Using Listing the Common Factors
Listing the factors of numbers is an easy method. We need to list all the factors of the numbers and find out the common factors between these numbers. Let’s find the GCF of 8 and 12 by listing the factors of both the numbers and then finding the common factor.
- Factors of 8 are 1, 2, 4, and 8.
- Factors of 12 are 1, 2, 3, 4, 6, and 12.
4 is the GCF of 8 and 12, as it is the largest common factor in both the factors list.
GCF of 8 and 12 Using Prime Factorization
Prime factorization is the method of breaking down any number into its prime factors. The prime numbers that are common to both numbers will be multiplied together to get the GCF of the numbers.
Here, we find the GCF of 8 and 12 using prime factorization
Prime factorization of 8 = 2 × 2 × 2 = 23
Prime factorization of 12 = 2 × 2 × 3 = 22 × 31
GCF of 8 and 12 = 2 × 2 = 4.
GCF of 8 and 12 Using Division Method
The division method can be done by taking the large number as the dividend and the small number as the divisor. Take the remainder as the new divisor and make the previous divisor as the dividend. Divide it until the remainder becomes 0.
Division method to find the GCF of 8 and 12.
Step 1: Take the large number (12) as the dividend and the small number (8) as divisor.
Step 2: By dividing the numbers, 12 / 8, we get 4 as remainder and quotient as 1.
Step 3: Take the remainder (4) as the new divisor and the previous divisor (8) as the dividend.
Step 4: The division is continued further till the remainder is 0.
When the remainder is 0, we consider the last divisor as the GCF. Therefore, the GCF of 8 and 12 is 4.
Common Mistakes and How to Avoid Them in GCF of 8 and 12
While solving GCF, children make mistakes like considering the power of the same factor twice. Just to avoid these mistakes, few solutions are discussed below -
Mistake 1
Not including 1 as a factor of any number.
Students must learn that 1 is a universal factor for all the numbers. It must be included in the list of factors all the time. The factors of 8 are 1, 2, 4 and 8.
Highest Common Factor of 8 and 12 Examples
Problem 1
If one number is 8, and the GCF with another number, ‘b’ is 4 and the LCM of the two numbers is 24, find the other number.
GCF x LCM = Product of the Numbers
4 x 24 = 8 x b
96 = 8 x b
b = 96 ÷ 8 = 12
Explanation
The equation GCF x LCM = Product of the Numbers, is taken and then solved to find the value of ‘b’. The value of b is 12.
Problem 2
If x is the GCF of 8 and 12 and solve 8x + 12x.
GCF of 8 and 12
Factors of 8 = 1, 2, 4, and 8.
Factors of 12 = 1, 2, 3, 4, 6, and 12.
Therefore, GCF = 4
Substituting 4 into the equation, x = 4.
8x + 12x
= 8 x 4 + 12 x 4
= 32 + 48
= 80.
Explanation
The GCF of 8 and 12 is to be found, and the value is to be substituted into the equation 8x + 12x, the result will be 80.
Problem 3
Simplify the fraction of 8/12 using the GCF.
The GCF of 8 and 12 is to be found.
Prime factorization of 8 = 2 × 2 × 2 = 23
Prime factorization of 12 = 2 × 2 × 3 = 22 × 31
GCF of 8 and 12 = 2 x 2 = 4.
Divide the numerator and denominator by 4
8/12 = 8 ÷ 4 / 12 ÷ 4
= 2/3
Explanation
The GCF of 8 and 12 is found by prime factorization. The fraction 8/12 is then divided by 4 on both numerator and denominator. The fraction will be â…”.
Problem 4
Frank has 8 apples and 12 oranges. He wants to divide them into equal groups with no remainder. What is the largest number of groups he can form
GCF of 8 and 12 is to be found
Factors of 8 = 1, 2, 4, and 8.
Factors of 12 = 1, 2, 3, 4, 6, and 12.
Therefore, GCF = 4
Number of apples each group will have = 8 ÷ 4 = 2
Number of oranges each group will have = 12 ÷ 4 = 3.
Explanation
The GCF to be found of 8 and 12, is 4. The number of apples and oranges each group will have is found by dividing 8 and 12 by 4. Each group will have 2 apples and 3 oranges
Problem 5
A factory packs 8 containers in one box and 12 in another. What is the largest number of containers that can be repacked into boxes with the same number of containers in each, without mixing?
The GCF of 8 and 12 is to be found
Factors of 8 = 1, 2, 4, and 8.
Factors of 12 = 1, 2, 3, 4, 6, and 12.
Therefore, GCF = 4
Thus, the number of containers that will be packed into each box will be 4.
Explanation
To find the number of containers that can be packed into each box without any mix up will be the GCF of 8 and 12. The GCF will be 4.
FAQs on Greatest Common Factor of 8 and 12
1.What is the product of GCF and LCM of 8 and 12?
2.Can 1 be GCF?
3.What is the HCF of 8 and 12?
4.Are GCF, HCF, and GCD the same?
5.Can 0 be GCF?
6.How can children in Philippines use numbers in everyday life to understand GCF of 8 and 12?
7.What are some fun ways kids in Philippines can practice GCF of 8 and 12 with numbers?
8.What role do numbers and GCF of 8 and 12 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve GCF of 8 and 12 skills?
Important Glossaries for GCF of 8 and 12
- GCD: The Greatest Common Divisor or the largest number that is an integer and has the ability to divide two or more numbers. For example, GCF of 8 and 12 is 4.
- Prime Factors: Prime factors of a number are the prime numbers that will be multiplied together to result in the original number. For example, the prime factors of 12 are 2 × 2 × 3 = 12.
- Co-prime Numbers: Two numbers are called co-prime numbers if 1 is their only common factor. For example, in 5 and 7, the only common factor is 1.
- Remainder: A remainder is the value that is left over after performing the division. For example, if 8 is divided by 5, we get 3 as remainder and 1 as quotient.
- Dividend: The number that is getting divided by another number. For example, if 12 is divided by 5, 12 is the dividend.
- Divisor: The number that divides the other number is called the divisor. For example, if 2 is divided by 5, 5 is the divisor
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
