How to Find GCF of 4975/64, 7000/770?

GCF of 4975/64, 7000/770

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 4975/64, 7000/770 i.e 25/24640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4975/64, 7000/770.

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 4975/64,7000/770?

Given fractions are 4975/64,7000/770

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 4975/64,7000/770, numerators are 4975,7000

Denominators are 64,770

The GCF of 4975,7000 is 25 .

LCM of 64,770 is 24640.

The greatest common factor of 4975/64,7000/770 = [GCF of 4975,7000]/[LCM of 64,770]= 25/24640

Therefore, the GCF of 4975/64,7000/770 is 25/24640.

Greatest Common Factor of 4975,7000

To find the highest common factor of 4975,7000, we have to find the factors of both numbers and list the highest common factor.

The factors of 4975 are 1, 5, 25, 199, 995, 4975

The factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, 7000

The HCF of 4975,7000 is 25.

Lets's calculate GCF of 4975,7000

Greatest Common Factor (GCF) of 4975,7000 By Common Division

5	4975, 7000
5	995, 1400
	199, 280

∴ So the GCF of the given numbers is 5 x 5 = 25

Greatest Common Factor of 4975,7000 By Matching Biggest Common Factor Method

Now, list down the factors of 4975

1,5,25,199,995,4975

Now, list down the factors of 7000

1,2,4,5,7,8,10,14,20,25,28,35,40,50,56,70,100,125,140,175,200,250,280,350,500,700,875,1000,1400,1750,3500,7000

Greatest Common Factor

We found the factors 4975,7000 . The biggest common factor number is the GCF number.
So the greatest common factor 4975,7000 is 25.

Lets's calculate LCM of 64,770

Lowest Common Multiple of 64,770 using Common Division

2	64, 770
	32, 385

∴ So the LCM of the given numbers is 2 x 32 x 385 = 24640

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/24640

Therefore, the GCF of Fractions 4975/64,7000/770 is 25/24640

Least Common Multiple of 64,770 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 64,770 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(64,770) = 2

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

GCF(64,770) x common factors =2 x 1 = 2

LCM(64,770) = ( 64 × 770 ) / 2

LCM(64,770) = 49280 / 2

LCM(64,770) = 24640

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FAQs on GCF of Fractions of 4975/64, 7000/770

1. What is the HCF of 4975,7000?

The HCF of 4975,7000 is 25

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 4975/64, 7000/770?

Answer: GCF of Numerators as per given numbers 4975/64, 7000/770 is

GCF of Numerators i.e. for 4975,7000 is 25

LCM of denominators i.e. for 64,770 is 24640.

Thus, GCF of Fractions is 25/24640.Finally, GCF of Fractions for 4975/64, 7000/770 is 25/24640.