GCF of 5460/251, 6540/6751
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5460/251, 6540/6751 i.e 60/1694501 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5460/251, 6540/6751.
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 5460/251,6540/6751?
Given fractions are 5460/251,6540/6751
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 5460/251,6540/6751, numerators are 5460,6540
Denominators are 251,6751
The GCF of 5460,6540 is 60 .
LCM of 251,6751 is 1694501.
The greatest common factor of 5460/251,6540/6751 = [GCF of 5460,6540]/[LCM of 251,6751]= 60/1694501
Therefore, the GCF of 5460/251,6540/6751 is 60/1694501.
To find the highest common factor of 5460,6540, we have to find the factors of both numbers and list the highest common factor.
The factors of 5460 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460
The factors of 6540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 109, 218, 327, 436, 545, 654, 1090, 1308, 1635, 2180, 3270, 6540
The HCF of 5460,6540 is 60.
Lets's calculate GCF of 5460,6540
| 2 | 5460, 6540 |
| 2 | 2730, 3270 |
| 3 | 1365, 1635 |
| 5 | 455, 545 |
| 91, 109 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 5460,6540 By Matching Biggest Common Factor Method
Now, list down the factors of 5460
:1,2,3,4,5,6,7,10,12,13,14,15,20,21,26,28,30,35,39,42,52,60,65,70,78,84,91,105,130,140,156,182,195,210,260,273,364,390,420,455,546,780,910,1092,1365,1820,2730,5460
Now, list down the factors of 6540
:1,2,3,4,5,6,10,12,15,20,30,60,109,218,327,436,545,654,1090,1308,1635,2180,3270,6540
Greatest Common Factor
We found the factors 5460,6540 . The biggest common factor number is the GCF number.
So the greatest common factor 5460,6540 is 60.
Lets's calculate LCM of 251,6751
Given numbers has no common factors except 1. So, there LCM is their product i.e 1694501
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/1694501
Therefore, the GCF of Fractions 5460/251,6540/6751 is 60/1694501
Least Common Multiple of 251,6751 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 251,6751 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(251,6751) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(251,6751) x common factors =1 x 1 = 1
LCM(251,6751) = ( 251 × 6751 ) / 1
LCM(251,6751) = 1694501 / 1
LCM(251,6751) = 1694501
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FAQs on GCF of Fractions of 5460/251, 6540/6751
1. What is the HCF of 5460,6540?
The HCF of 5460,6540 is 60
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 5460/251, 6540/6751?
Answer: GCF of Numerators as per given numbers 5460/251, 6540/6751 is
GCF of Numerators i.e. for 5460,6540 is 60
LCM of denominators i.e. for 251,6751 is 1694501.
Thus, GCF of Fractions is 60/1694501.Finally, GCF of Fractions for 5460/251, 6540/6751 is 60/1694501.