How to Find GCF of 7870/408, 3177/7200?

GCF of 7870/408, 3177/7200

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 7870/408, 3177/7200 i.e 1/122400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7870/408, 3177/7200.

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 7870/408,3177/7200?

Given fractions are 7870/408,3177/7200

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 7870/408,3177/7200, numerators are 7870,3177

Denominators are 408,7200

The GCF of 7870,3177 is 1 .

LCM of 408,7200 is 122400.

The greatest common factor of 7870/408,3177/7200 = [GCF of 7870,3177]/[LCM of 408,7200]= 1/122400

Therefore, the GCF of 7870/408,3177/7200 is 1/122400.

Greatest Common Factor of 7870,3177

To find the highest common factor of 7870,3177, 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 3177 are 1, 3, 9, 353, 1059, 3177

The HCF of 7870,3177 is 1.

Lets's calculate GCF of 7870,3177

Greatest Common Factor (GCF) of 7870,3177 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 7870,3177 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 3177

1,3,9,353,1059,3177

Greatest Common Factor

We found the factors 7870,3177 . The biggest common factor number is the GCF number.
So the greatest common factor 7870,3177 is 1.

Lets's calculate LCM of 408,7200

Lowest Common Multiple of 408,7200 using Common Division

2	408, 7200
2	204, 3600
2	102, 1800
3	51, 900
	17, 300

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 17 x 300 = 122400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/122400

Therefore, the GCF of Fractions 7870/408,3177/7200 is 1/122400

Least Common Multiple of 408,7200 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 408,7200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(408,7200) = 24

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

GCF(408,7200) x common factors =24 x 1 = 24

LCM(408,7200) = ( 408 × 7200 ) / 24

LCM(408,7200) = 2937600 / 24

LCM(408,7200) = 122400

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FAQs on GCF of Fractions of 7870/408, 3177/7200

1. What is the HCF of 7870,3177?

The HCF of 7870,3177 is 1

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 7870/408, 3177/7200?

Answer: GCF of Numerators as per given numbers 7870/408, 3177/7200 is

GCF of Numerators i.e. for 7870,3177 is 1

LCM of denominators i.e. for 408,7200 is 122400.

Thus, GCF of Fractions is 1/122400.Finally, GCF of Fractions for 7870/408, 3177/7200 is 1/122400.