GCF of 624/68, 768/364
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 624/68, 768/364 i.e 48/6188 easily. The following is the detailed procedure to determine the greatest common factor of fractions 624/68, 768/364.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 624/68,768/364?
Given fractions are 624/68,768/364
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 624/68,768/364, numerators are 624,768
Denominators are 68,364
The GCF of 624,768 is 48 .
LCM of 68,364 is 6188.
The greatest common factor of 624/68,768/364 = [GCF of 624,768]/[LCM of 68,364]= 48/6188
Therefore, the GCF of 624/68,768/364 is 48/6188.
To find the highest common factor of 624,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 624,768 is 48.
Lets's calculate GCF of 624,768
| 2 | 624, 768 |
| 2 | 312, 384 |
| 2 | 156, 192 |
| 2 | 78, 96 |
| 3 | 39, 48 |
| 13, 16 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 = 48
Greatest Common Factor of 624,768 By Matching Biggest Common Factor Method
Now, list down the factors of 624
:1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 624,768 . The biggest common factor number is the GCF number.
So the greatest common factor 624,768 is 48.
Lets's calculate LCM of 68,364
| 2 | 68, 364 |
| 2 | 34, 182 |
| 17, 91 |
∴ So the LCM of the given numbers is 2 x 2 x 17 x 91 = 6188
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 48/6188
Therefore, the GCF of Fractions 624/68,768/364 is 48/6188
Least Common Multiple of 68,364 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 68,364 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,364) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(68,364) x common factors =4 x 1 = 4
LCM(68,364) = ( 68 × 364 ) / 4
LCM(68,364) = 24752 / 4
LCM(68,364) = 6188
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 624/68, 768/364
1. What is the HCF of 624,768?
The HCF of 624,768 is 48
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 624/68, 768/364?
Answer: GCF of Numerators as per given numbers 624/68, 768/364 is
GCF of Numerators i.e. for 624,768 is 48
LCM of denominators i.e. for 68,364 is 6188.
Thus, GCF of Fractions is 48/6188.Finally, GCF of Fractions for 624/68, 768/364 is 48/6188.