How to Find GCF of 7772/360, 3874/6250?

GCF of 7772/360, 3874/6250

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 7772/360, 3874/6250 i.e 2/225000 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7772/360, 3874/6250.

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 7772/360,3874/6250?

Given fractions are 7772/360,3874/6250

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 7772/360,3874/6250, numerators are 7772,3874

Denominators are 360,6250

The GCF of 7772,3874 is 2 .

LCM of 360,6250 is 225000.

The greatest common factor of 7772/360,3874/6250 = [GCF of 7772,3874]/[LCM of 360,6250]= 2/225000

Therefore, the GCF of 7772/360,3874/6250 is 2/225000.

Greatest Common Factor of 7772,3874

To find the highest common factor of 7772,3874, we have to find the factors of both numbers and list the highest common factor.

The factors of 7772 are 1, 2, 4, 29, 58, 67, 116, 134, 268, 1943, 3886, 7772

The factors of 3874 are 1, 2, 13, 26, 149, 298, 1937, 3874

The HCF of 7772,3874 is 2.

Lets's calculate GCF of 7772,3874

Greatest Common Factor (GCF) of 7772,3874 By Common Division

2	7772, 3874
	3886, 1937

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 7772,3874 By Matching Biggest Common Factor Method

Now, list down the factors of 7772

1,2,4,29,58,67,116,134,268,1943,3886,7772

Now, list down the factors of 3874

1,2,13,26,149,298,1937,3874

Greatest Common Factor

We found the factors 7772,3874 . The biggest common factor number is the GCF number.
So the greatest common factor 7772,3874 is 2.

Lets's calculate LCM of 360,6250

Lowest Common Multiple of 360,6250 using Common Division

2	360, 6250
5	180, 3125
	36, 625

∴ So the LCM of the given numbers is 2 x 5 x 36 x 625 = 225000

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/225000

Therefore, the GCF of Fractions 7772/360,3874/6250 is 2/225000

Least Common Multiple of 360,6250 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 360,6250 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(360,6250) = 10

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

GCF(360,6250) x common factors =10 x 1 = 10

LCM(360,6250) = ( 360 × 6250 ) / 10

LCM(360,6250) = 2250000 / 10

LCM(360,6250) = 225000

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FAQs on GCF of Fractions of 7772/360, 3874/6250

1. What is the HCF of 7772,3874?

The HCF of 7772,3874 is 2

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 7772/360, 3874/6250?

Answer: GCF of Numerators as per given numbers 7772/360, 3874/6250 is

GCF of Numerators i.e. for 7772,3874 is 2

LCM of denominators i.e. for 360,6250 is 225000.

Thus, GCF of Fractions is 2/225000.Finally, GCF of Fractions for 7772/360, 3874/6250 is 2/225000.