GCF of 76/364, 42/504, 280/864
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 76/364, 42/504, 280/864 i.e 2/78624 easily. The following is the detailed procedure to determine the greatest common factor of fractions 76/364, 42/504, 280/864.
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 76/364,42/504,280/864?
Given fractions are 76/364,42/504,280/864
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 76/364,42/504,280/864, numerators are 76,42,280
Denominators are 364,504,864
The GCF of 76,42,280 is 2 .
LCM of 364,504,864 is 78624.
The greatest common factor of 76/364,42/504,280/864 = [GCF of 76,42,280]/[LCM of 364,504,864]= 2/78624
Therefore, the GCF of 76/364,42/504,280/864 is 2/78624.
To find the highest common factor of 76,42,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 76,42,280 is 2.
Lets's calculate GCF of 76,42,280
| 2 | 76, 42, 280 |
| 38, 21, 140 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 76,42,280 By Matching Biggest Common Factor Method
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 76,42,280 . The biggest common factor number is the GCF number.
So the greatest common factor 76,42,280 is 2.
Lets's calculate LCM of 364,504,864
| 2 | 364, 504, 864 |
| 2 | 182, 252, 432 |
| 2 | 91, 126, 216 |
| 3 | 91, 63, 108 |
| 3 | 91, 21, 36 |
| 7 | 91, 7, 12 |
| 13, 1, 12 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 3 x 7 x 13 x 1 x 12 = 78624
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/78624
Therefore, the GCF of Fractions 76/364,42/504,280/864 is 2/78624
Least Common Multiple of 364,504,864 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 364,504,864 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(364,504,864) = 4
common factors(in case of two or more numbers have common factors) = 504
GCF(364,504,864) x common factors =4 x 504 = 2016
LCM(364,504,864) = ( 364 × 504 × 864 ) / 2016
LCM(364,504,864) = 158505984 / 2016
LCM(364,504,864) = 78624
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FAQs on GCF of Fractions of 76/364, 42/504, 280/864
1. What is the HCF of 76,42,280?
The HCF of 76,42,280 is 2
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 76/364, 42/504, 280/864?
Answer: GCF of Numerators as per given numbers 76/364, 42/504, 280/864 is
GCF of Numerators i.e. for 76,42,280 is 2
LCM of denominators i.e. for 364,504,864 is 78624.
Thus, GCF of Fractions is 2/78624.Finally, GCF of Fractions for 76/364, 42/504, 280/864 is 2/78624.