GCF of 24 and 28
GCF of 24 and 28
The greatest common factor (GCF) of 24 and 28 is 4. To find the GCF, we first identify the factors of each number. For 24, its factors are 1, 2, 3, 4, 6, 8, 12, and 24. For 28, its factors are 1, 2, 4, 7, 14, and 28. The highest common factor among these two sets of factors is 4, which means it’s the largest numbers that divides both 24 and 28 without leaving a remainder. So, 4 is the GCF of 24 and 28.
GCF of 24 and 28
GCF of 24 and 28 is 4.
Methods to Find GCF of 24 and 28
- Prime Factorization Method
- Long Division Method
- Listing Common Factors
GCF of 24 and 28 by Prime Factorization Method.
Step 1: Find the prime factors of each number.
Prime factors of 24: 2 x 2 x 2 x 3
Prime factors of 28: 2 x 2 x 7
Step 2: Identify the common prime factors.
- Common prime factors: 2 x 2
Step 3: Multiply the common prime factors.
GCF = 2 x 2 = 4
So, the greatest common factor of 24 and 28 is 4.
GCF of 24 and 28 by Long Division Method.
To find the Greatest Common Factor (GCF) of 24 and 28 using the Long Division Method, follow these simple steps:
Step-by-Step Process:
Divide the Larger Number by the Smaller Number:
Divide 28 (larger number) by 24 (smaller number).
28 ÷ 24 = 1 remainder 4
Replace the Larger Number with the Smaller Number:
The divisors (24) becomes the new dividend.
The remainder (4) becomes the new divisor.
Repeat the Division:
Now, divide 24 by 4.
24 ÷ 4 = 6 remainder 0
Check the Remainder:
When the remainder is 0, the current divisor is the GCF.
The remainder is 0, and the current divisor is 4.
GCF of 24 and 28 by Listing Common Factors.
List the Factors of Each Number:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 28: 1, 2, 4, 7, 14, 28
Identify the Common Factors:
- The common factors of 24 and 28 are: 1, 2, 4
Find the Greatest Common Factor:
The largest number in the list of common factors is 4.
What is the GCF of 28?
The Greatest Common Factor (GCF) of a single number, like 28, is the number itself. Thus, the GCF of 28 is 28, as it is the largest factor.
Gcf of 24 and 28 calculator
To find the GCF of 24 and 28 using a calculator, input both numbers into the GCF function. The calculator will output 4, as 4 is the greatest common factor.
Gcf of 24 and 28 worksheet
A worksheet on finding the GCF of 24 and 28 includes exercises on listing factors, using the long division method, and finding common factors to determine that the GCF is 4.
Can the GCF of 24 and 28 be found using the Euclidean algorithm?
Yes, the Euclidean algorithm involves repeated division. Divide 28 by 24, get the remainder 4, then divide 24 by 4 to get a remainder of 0. The GCF is 4.
What is the relationship between the GCF and LCM of 24 and 28?
The product of the GCF and LCM of two numbers equals the product of the numbers. For 24 and 28: GCF × LCM = 24 × 28.
Can you find the GCF of 24 and 28 by inspection?
Yes, by observing that both numbers share common factors 1, 2, and 4, you can determine that the largest common factor is 4.
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