GCF of 980/272, 1680/618
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 980/272, 1680/618 i.e 140/84048 easily. The following is the detailed procedure to determine the greatest common factor of fractions 980/272, 1680/618.
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 980/272,1680/618?
Given fractions are 980/272,1680/618
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 980/272,1680/618, numerators are 980,1680
Denominators are 272,618
The GCF of 980,1680 is 140 .
LCM of 272,618 is 84048.
The greatest common factor of 980/272,1680/618 = [GCF of 980,1680]/[LCM of 272,618]= 140/84048
Therefore, the GCF of 980/272,1680/618 is 140/84048.
To find the highest common factor of 980,1680, we have to find the factors of both numbers and list the highest common factor.
The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
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 HCF of 980,1680 is 140.
Lets's calculate GCF of 980,1680
| 2 | 980, 1680 |
| 2 | 490, 840 |
| 5 | 245, 420 |
| 7 | 49, 84 |
| 7, 12 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 7 = 140
Greatest Common Factor of 980,1680 By Matching Biggest Common Factor Method
Now, list down the factors of 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
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
Greatest Common Factor
We found the factors 980,1680 . The biggest common factor number is the GCF number.
So the greatest common factor 980,1680 is 140.
Lets's calculate LCM of 272,618
| 2 | 272, 618 |
| 136, 309 |
∴ So the LCM of the given numbers is 2 x 136 x 309 = 84048
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 140/84048
Therefore, the GCF of Fractions 980/272,1680/618 is 140/84048
Least Common Multiple of 272,618 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 272,618 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(272,618) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(272,618) x common factors =2 x 1 = 2
LCM(272,618) = ( 272 × 618 ) / 2
LCM(272,618) = 168096 / 2
LCM(272,618) = 84048
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FAQs on GCF of Fractions of 980/272, 1680/618
1. What is the HCF of 980,1680?
The HCF of 980,1680 is 140
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 980/272, 1680/618?
Answer: GCF of Numerators as per given numbers 980/272, 1680/618 is
GCF of Numerators i.e. for 980,1680 is 140
LCM of denominators i.e. for 272,618 is 84048.
Thus, GCF of Fractions is 140/84048.Finally, GCF of Fractions for 980/272, 1680/618 is 140/84048.