How to Find GCF of 7870/689, 6030/857?

GCF of 7870/689, 6030/857

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 7870/689, 6030/857 i.e 10/590473 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7870/689, 6030/857.

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 7870/689,6030/857?

Given fractions are 7870/689,6030/857

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 7870/689,6030/857, numerators are 7870,6030

Denominators are 689,857

The GCF of 7870,6030 is 10 .

LCM of 689,857 is 590473.

The greatest common factor of 7870/689,6030/857 = [GCF of 7870,6030]/[LCM of 689,857]= 10/590473

Therefore, the GCF of 7870/689,6030/857 is 10/590473.

Greatest Common Factor of 7870,6030

To find the highest common factor of 7870,6030, we have to find the factors of both numbers and list the highest common factor.

The factors of 7870 are 1, 2, 5, 10, 787, 1574, 3935, 7870

The factors of 6030 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 67, 90, 134, 201, 335, 402, 603, 670, 1005, 1206, 2010, 3015, 6030

The HCF of 7870,6030 is 10.

Lets's calculate GCF of 7870,6030

Greatest Common Factor (GCF) of 7870,6030 By Common Division

2	7870, 6030
5	3935, 3015
	787, 603

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 7870,6030 By Matching Biggest Common Factor Method

Now, list down the factors of 7870

1,2,5,10,787,1574,3935,7870

Now, list down the factors of 6030

1,2,3,5,6,9,10,15,18,30,45,67,90,134,201,335,402,603,670,1005,1206,2010,3015,6030

Greatest Common Factor

We found the factors 7870,6030 . The biggest common factor number is the GCF number.
So the greatest common factor 7870,6030 is 10.

Lets's calculate LCM of 689,857

Lowest Common Multiple of 689,857 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 590473

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/590473

Therefore, the GCF of Fractions 7870/689,6030/857 is 10/590473

Least Common Multiple of 689,857 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 689,857 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(689,857) = 1

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

GCF(689,857) x common factors =1 x 1 = 1

LCM(689,857) = ( 689 × 857 ) / 1

LCM(689,857) = 590473 / 1

LCM(689,857) = 590473

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FAQs on GCF of Fractions of 7870/689, 6030/857

1. What is the HCF of 7870,6030?

The HCF of 7870,6030 is 10

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 7870/689, 6030/857?

Answer: GCF of Numerators as per given numbers 7870/689, 6030/857 is

GCF of Numerators i.e. for 7870,6030 is 10

LCM of denominators i.e. for 689,857 is 590473.

Thus, GCF of Fractions is 10/590473.Finally, GCF of Fractions for 7870/689, 6030/857 is 10/590473.