GCF of 432/74, 768/312
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 432/74, 768/312 i.e 48/11544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 432/74, 768/312.
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 432/74,768/312?
Given fractions are 432/74,768/312
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 432/74,768/312, numerators are 432,768
Denominators are 74,312
The GCF of 432,768 is 48 .
LCM of 74,312 is 11544.
The greatest common factor of 432/74,768/312 = [GCF of 432,768]/[LCM of 74,312]= 48/11544
Therefore, the GCF of 432/74,768/312 is 48/11544.
To find the highest common factor of 432,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 432 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432
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 432,768 is 48.
Lets's calculate GCF of 432,768
| 2 | 432, 768 |
| 2 | 216, 384 |
| 2 | 108, 192 |
| 2 | 54, 96 |
| 3 | 27, 48 |
| 9, 16 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 = 48
Greatest Common Factor of 432,768 By Matching Biggest Common Factor Method
Now, list down the factors of 432
:1,2,3,4,6,8,9,12,16,18,24,27,36,48,54,72,108,144,216,432
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 432,768 . The biggest common factor number is the GCF number.
So the greatest common factor 432,768 is 48.
Lets's calculate LCM of 74,312
| 2 | 74, 312 |
| 37, 156 |
∴ So the LCM of the given numbers is 2 x 37 x 156 = 11544
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 48/11544
Therefore, the GCF of Fractions 432/74,768/312 is 48/11544
Least Common Multiple of 74,312 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 74,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,312) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,312) x common factors =2 x 1 = 2
LCM(74,312) = ( 74 × 312 ) / 2
LCM(74,312) = 23088 / 2
LCM(74,312) = 11544
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FAQs on GCF of Fractions of 432/74, 768/312
1. What is the HCF of 432,768?
The HCF of 432,768 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 432/74, 768/312?
Answer: GCF of Numerators as per given numbers 432/74, 768/312 is
GCF of Numerators i.e. for 432,768 is 48
LCM of denominators i.e. for 74,312 is 11544.
Thus, GCF of Fractions is 48/11544.Finally, GCF of Fractions for 432/74, 768/312 is 48/11544.