How to Find GCF of 6225/784, 2986/104?

GCF of 6225/784, 2986/104

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 6225/784, 2986/104 i.e 1/10192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6225/784, 2986/104.

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 6225/784,2986/104?

Given fractions are 6225/784,2986/104

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 6225/784,2986/104, numerators are 6225,2986

Denominators are 784,104

The GCF of 6225,2986 is 1 .

LCM of 784,104 is 10192.

The greatest common factor of 6225/784,2986/104 = [GCF of 6225,2986]/[LCM of 784,104]= 1/10192

Therefore, the GCF of 6225/784,2986/104 is 1/10192.

Greatest Common Factor of 6225,2986

To find the highest common factor of 6225,2986, we have to find the factors of both numbers and list the highest common factor.

The factors of 6225 are 1, 3, 5, 15, 25, 75, 83, 249, 415, 1245, 2075, 6225

The factors of 2986 are 1, 2, 1493, 2986

The HCF of 6225,2986 is 1.

Lets's calculate GCF of 6225,2986

Greatest Common Factor (GCF) of 6225,2986 By Common Division

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

Greatest Common Factor of 6225,2986 By Matching Biggest Common Factor Method

Now, list down the factors of 6225

1,3,5,15,25,75,83,249,415,1245,2075,6225

Now, list down the factors of 2986

1,2,1493,2986

Greatest Common Factor

We found the factors 6225,2986 . The biggest common factor number is the GCF number.
So the greatest common factor 6225,2986 is 1.

Lets's calculate LCM of 784,104

Lowest Common Multiple of 784,104 using Common Division

2	784, 104
2	392, 52
2	196, 26
	98, 13

∴ So the LCM of the given numbers is 2 x 2 x 2 x 98 x 13 = 10192

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10192

Therefore, the GCF of Fractions 6225/784,2986/104 is 1/10192

Least Common Multiple of 784,104 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 784,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(784,104) = 8

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

GCF(784,104) x common factors =8 x 1 = 8

LCM(784,104) = ( 784 × 104 ) / 8

LCM(784,104) = 81536 / 8

LCM(784,104) = 10192

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FAQs on GCF of Fractions of 6225/784, 2986/104

1. What is the HCF of 6225,2986?

The HCF of 6225,2986 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 6225/784, 2986/104?

Answer: GCF of Numerators as per given numbers 6225/784, 2986/104 is

GCF of Numerators i.e. for 6225,2986 is 1

LCM of denominators i.e. for 784,104 is 10192.

Thus, GCF of Fractions is 1/10192.Finally, GCF of Fractions for 6225/784, 2986/104 is 1/10192.