How to Find GCF of 644/83, 616/974?

GCF of 644/83, 616/974

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 644/83, 616/974 i.e 28/80842 easily. The following is the detailed procedure to determine the greatest common factor of fractions 644/83, 616/974.

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 644/83,616/974?

Given fractions are 644/83,616/974

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 644/83,616/974, numerators are 644,616

Denominators are 83,974

The GCF of 644,616 is 28 .

LCM of 83,974 is 80842.

The greatest common factor of 644/83,616/974 = [GCF of 644,616]/[LCM of 83,974]= 28/80842

Therefore, the GCF of 644/83,616/974 is 28/80842.

Greatest Common Factor of 644,616

To find the highest common factor of 644,616, we have to find the factors of both numbers and list the highest common factor.

The factors of 644 are 1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644

The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616

The HCF of 644,616 is 28.

Lets's calculate GCF of 644,616

Greatest Common Factor (GCF) of 644,616 By Common Division

2	644, 616
2	322, 308
7	161, 154
	23, 22

∴ So the GCF of the given numbers is 2 x 2 x 7 = 28

Greatest Common Factor of 644,616 By Matching Biggest Common Factor Method

Now, list down the factors of 644

1,2,4,7,14,23,28,46,92,161,322,644

Now, list down the factors of 616

1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616

Greatest Common Factor

We found the factors 644,616 . The biggest common factor number is the GCF number.
So the greatest common factor 644,616 is 28.

Lets's calculate LCM of 83,974

Lowest Common Multiple of 83,974 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 80842

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/80842

Therefore, the GCF of Fractions 644/83,616/974 is 28/80842

Least Common Multiple of 83,974 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 83,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,974) = 1

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

GCF(83,974) x common factors =1 x 1 = 1

LCM(83,974) = ( 83 × 974 ) / 1

LCM(83,974) = 80842 / 1

LCM(83,974) = 80842

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FAQs on GCF of Fractions of 644/83, 616/974

1. What is the HCF of 644,616?

The HCF of 644,616 is 28

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 644/83, 616/974?

Answer: GCF of Numerators as per given numbers 644/83, 616/974 is

GCF of Numerators i.e. for 644,616 is 28

LCM of denominators i.e. for 83,974 is 80842.

Thus, GCF of Fractions is 28/80842.Finally, GCF of Fractions for 644/83, 616/974 is 28/80842.