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GCF of 780/840, 1671/825

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 780/840, 1671/825 i.e 3/46200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 780/840, 1671/825.

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 780/840,1671/825?

Given fractions are 780/840,1671/825

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 780/840,1671/825, numerators are 780,1671

Denominators are 840,825

The GCF of 780,1671 is 3 .

LCM of 840,825 is 46200.

The greatest common factor of 780/840,1671/825 = [GCF of 780,1671]/[LCM of 840,825]= 3/46200

Therefore, the GCF of 780/840,1671/825 is 3/46200.

Greatest Common Factor of 780,1671

To find the highest common factor of 780,1671, we have to find the factors of both numbers and list the highest common factor.

The factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780

The factors of 1671 are 1, 3, 557, 1671

The HCF of 780,1671 is 3.

Lets's calculate GCF of 780,1671

Greatest Common Factor (GCF) of 780,1671 By Common Division

3 780, 1671
260, 557

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 780,1671 By Matching Biggest Common Factor Method

Greatest Common Factor of 780,1671 By Matching Biggest Common Factor Method

Now, list down the factors of 780

:

1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780

Now, list down the factors of 1671

:

1,3,557,1671

Greatest Common Factor

We found the factors 780,1671 . The biggest common factor number is the GCF number.
So the greatest common factor 780,1671 is 3.


Lets's calculate LCM of 840,825

Lowest Common Multiple of 840,825 using Common Division

3 840, 825
5 280, 275
56, 55

∴ So the LCM of the given numbers is 3 x 5 x 56 x 55 = 46200

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/46200

Therefore, the GCF of Fractions 780/840,1671/825 is 3/46200

Least Common Multiple of 840,825 with GCF Formula

Least Common Multiple of 840,825 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 840,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(840,825) = 15

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

GCF(840,825) x common factors =15 x 1 = 15

LCM(840,825) = ( 840 × 825 ) / 15

LCM(840,825) = 693000 / 15

LCM(840,825) = 46200


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 780/840, 1671/825

1. What is the HCF of 780,1671?

The HCF of 780,1671 is 3

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 780/840, 1671/825?

Answer: GCF of Numerators as per given numbers 780/840, 1671/825 is

GCF of Numerators i.e. for 780,1671 is 3

LCM of denominators i.e. for 840,825 is 46200.

Thus, GCF of Fractions is 3/46200.Finally, GCF of Fractions for 780/840, 1671/825 is 3/46200.