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GCF of 840/35, 460/2814

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023


Use our free GCF of Fractions Calculator tool to compute the GCF of 840/35, 460/2814 i.e 20/14070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 840/35, 460/2814.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 840/35,460/2814?

Given fractions are 840/35,460/2814

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 840/35,460/2814, numerators are 840,460

Denominators are 35,2814

The GCF of 840,460 is 20 .

LCM of 35,2814 is 14070.

The greatest common factor of 840/35,460/2814 = [GCF of 840,460]/[LCM of 35,2814]= 20/14070

Therefore, the GCF of 840/35,460/2814 is 20/14070.

Greatest Common Factor of 840,460

To find the highest common factor of 840,460, 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 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460

The HCF of 840,460 is 20.

Lets's calculate GCF of 840,460

Greatest Common Factor (GCF) of 840,460 By Common Division

2 840, 460
2 420, 230
5 210, 115
42, 23

∴ So the GCF of the given numbers is 2 x 2 x 5 = 20

Greatest Common Factor of 840,460 By Matching Biggest Common Factor Method

Greatest Common Factor of 840,460 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 460

:

1,2,4,5,10,20,23,46,92,115,230,460

Greatest Common Factor

We found the factors 840,460 . The biggest common factor number is the GCF number.
So the greatest common factor 840,460 is 20.


Lets's calculate LCM of 35,2814

Lowest Common Multiple of 35,2814 using Common Division

7 35, 2814
5, 402

∴ So the LCM of the given numbers is 7 x 5 x 402 = 14070

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/14070

Therefore, the GCF of Fractions 840/35,460/2814 is 20/14070

Least Common Multiple of 35,2814 with GCF Formula

Least Common Multiple of 35,2814 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 35,2814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(35,2814) = 7

common factors(in case of two or more numbers have common factors) = 1

GCF(35,2814) x common factors =7 x 1 = 7

LCM(35,2814) = ( 35 × 2814 ) / 7

LCM(35,2814) = 98490 / 7

LCM(35,2814) = 14070


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 840/35, 460/2814

1. What is the HCF of 840,460?

The HCF of 840,460 is 20

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 840/35, 460/2814?

Answer: GCF of Numerators as per given numbers 840/35, 460/2814 is

GCF of Numerators i.e. for 840,460 is 20

LCM of denominators i.e. for 35,2814 is 14070.

Thus, GCF of Fractions is 20/14070.Finally, GCF of Fractions for 840/35, 460/2814 is 20/14070.