GCF of 537/78, 935/54, 420/76
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 537/78, 935/54, 420/76 i.e 1/26676 easily. The following is the detailed procedure to determine the greatest common factor of fractions 537/78, 935/54, 420/76.
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 537/78,935/54,420/76?
Given fractions are 537/78,935/54,420/76
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 537/78,935/54,420/76, numerators are 537,935,420
Denominators are 78,54,76
The GCF of 537,935,420 is 1 .
LCM of 78,54,76 is 26676.
The greatest common factor of 537/78,935/54,420/76 = [GCF of 537,935,420]/[LCM of 78,54,76]= 1/26676
Therefore, the GCF of 537/78,935/54,420/76 is 1/26676.
To find the highest common factor of 537,935,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 537 are 1, 3, 179, 537
The factors of 935 are 1, 5, 11, 17, 55, 85, 187, 935
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 537,935,420 is 1.
Lets's calculate GCF of 537,935,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 537,935,420 By Matching Biggest Common Factor Method
Now, list down the factors of 537
:1,3,179,537
Now, list down the factors of 935
:1,5,11,17,55,85,187,935
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 537,935,420 . The biggest common factor number is the GCF number.
So the greatest common factor 537,935,420 is 1.
Lets's calculate LCM of 78,54,76
| 2 | 78, 54, 76 |
| 3 | 39, 27, 38 |
| 13, 9, 38 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 9 x 38 = 26676
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26676
Therefore, the GCF of Fractions 537/78,935/54,420/76 is 1/26676
Least Common Multiple of 78,54,76 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 78,54,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,54,76) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(78,54,76) x common factors =2 x 6 = 12
LCM(78,54,76) = ( 78 × 54 × 76 ) / 12
LCM(78,54,76) = 320112 / 12
LCM(78,54,76) = 26676
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FAQs on GCF of Fractions of 537/78, 935/54, 420/76
1. What is the HCF of 537,935,420?
The HCF of 537,935,420 is 1
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 537/78, 935/54, 420/76?
Answer: GCF of Numerators as per given numbers 537/78, 935/54, 420/76 is
GCF of Numerators i.e. for 537,935,420 is 1
LCM of denominators i.e. for 78,54,76 is 26676.
Thus, GCF of Fractions is 1/26676.Finally, GCF of Fractions for 537/78, 935/54, 420/76 is 1/26676.