GCF of 840/219, 510/759
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 840/219, 510/759 i.e 30/55407 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/219, 510/759.
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 840/219,510/759?
Given fractions are 840/219,510/759
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 840/219,510/759, numerators are 840,510
Denominators are 219,759
The GCF of 840,510 is 30 .
LCM of 219,759 is 55407.
The greatest common factor of 840/219,510/759 = [GCF of 840,510]/[LCM of 219,759]= 30/55407
Therefore, the GCF of 840/219,510/759 is 30/55407.
To find the highest common factor of 840,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 840,510 is 30.
Lets's calculate GCF of 840,510
| 2 | 840, 510 |
| 3 | 420, 255 |
| 5 | 140, 85 |
| 28, 17 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 840,510 By Matching Biggest Common Factor Method
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Greatest Common Factor
We found the factors 840,510 . The biggest common factor number is the GCF number.
So the greatest common factor 840,510 is 30.
Lets's calculate LCM of 219,759
| 3 | 219, 759 |
| 73, 253 |
∴ So the LCM of the given numbers is 3 x 73 x 253 = 55407
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/55407
Therefore, the GCF of Fractions 840/219,510/759 is 30/55407
Least Common Multiple of 219,759 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 219,759 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(219,759) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(219,759) x common factors =3 x 1 = 3
LCM(219,759) = ( 219 × 759 ) / 3
LCM(219,759) = 166221 / 3
LCM(219,759) = 55407
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FAQs on GCF of Fractions of 840/219, 510/759
1. What is the HCF of 840,510?
The HCF of 840,510 is 30
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 840/219, 510/759?
Answer: GCF of Numerators as per given numbers 840/219, 510/759 is
GCF of Numerators i.e. for 840,510 is 30
LCM of denominators i.e. for 219,759 is 55407.
Thus, GCF of Fractions is 30/55407.Finally, GCF of Fractions for 840/219, 510/759 is 30/55407.