GCF of 1680/980, 6951/270
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1680/980, 6951/270 i.e 21/26460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1680/980, 6951/270.
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 1680/980,6951/270?
Given fractions are 1680/980,6951/270
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 1680/980,6951/270, numerators are 1680,6951
Denominators are 980,270
The GCF of 1680,6951 is 21 .
LCM of 980,270 is 26460.
The greatest common factor of 1680/980,6951/270 = [GCF of 1680,6951]/[LCM of 980,270]= 21/26460
Therefore, the GCF of 1680/980,6951/270 is 21/26460.
To find the highest common factor of 1680,6951, we have to find the factors of both numbers and list the highest common factor.
The factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680
The factors of 6951 are 1, 3, 7, 21, 331, 993, 2317, 6951
The HCF of 1680,6951 is 21.
Lets's calculate GCF of 1680,6951
| 3 | 1680, 6951 |
| 7 | 560, 2317 |
| 80, 331 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 1680,6951 By Matching Biggest Common Factor Method
Now, list down the factors of 1680
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,35,40,42,48,56,60,70,80,84,105,112,120,140,168,210,240,280,336,420,560,840,1680
Now, list down the factors of 6951
:1,3,7,21,331,993,2317,6951
Greatest Common Factor
We found the factors 1680,6951 . The biggest common factor number is the GCF number.
So the greatest common factor 1680,6951 is 21.
Lets's calculate LCM of 980,270
| 2 | 980, 270 |
| 5 | 490, 135 |
| 98, 27 |
∴ So the LCM of the given numbers is 2 x 5 x 98 x 27 = 26460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/26460
Therefore, the GCF of Fractions 1680/980,6951/270 is 21/26460
Least Common Multiple of 980,270 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 980,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(980,270) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(980,270) x common factors =10 x 1 = 10
LCM(980,270) = ( 980 × 270 ) / 10
LCM(980,270) = 264600 / 10
LCM(980,270) = 26460
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FAQs on GCF of Fractions of 1680/980, 6951/270
1. What is the HCF of 1680,6951?
The HCF of 1680,6951 is 21
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 1680/980, 6951/270?
Answer: GCF of Numerators as per given numbers 1680/980, 6951/270 is
GCF of Numerators i.e. for 1680,6951 is 21
LCM of denominators i.e. for 980,270 is 26460.
Thus, GCF of Fractions is 21/26460.Finally, GCF of Fractions for 1680/980, 6951/270 is 21/26460.