How to Find GCF of 828/687, 1220/662?

GCF of 828/687, 1220/662

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 828/687, 1220/662 i.e 4/454794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/687, 1220/662.

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 828/687,1220/662?

Given fractions are 828/687,1220/662

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 828/687,1220/662, numerators are 828,1220

Denominators are 687,662

The GCF of 828,1220 is 4 .

LCM of 687,662 is 454794.

The greatest common factor of 828/687,1220/662 = [GCF of 828,1220]/[LCM of 687,662]= 4/454794

Therefore, the GCF of 828/687,1220/662 is 4/454794.

Greatest Common Factor of 828,1220

To find the highest common factor of 828,1220, we have to find the factors of both numbers and list the highest common factor.

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828

The factors of 1220 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220

The HCF of 828,1220 is 4.

Lets's calculate GCF of 828,1220

Greatest Common Factor (GCF) of 828,1220 By Common Division

2	828, 1220
2	414, 610
	207, 305

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 828,1220 By Matching Biggest Common Factor Method

Now, list down the factors of 828

1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828

Now, list down the factors of 1220

1,2,4,5,10,20,61,122,244,305,610,1220

Greatest Common Factor

We found the factors 828,1220 . The biggest common factor number is the GCF number.
So the greatest common factor 828,1220 is 4.

Lets's calculate LCM of 687,662

Lowest Common Multiple of 687,662 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 454794

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/454794

Therefore, the GCF of Fractions 828/687,1220/662 is 4/454794

Least Common Multiple of 687,662 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 687,662 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(687,662) = 1

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

GCF(687,662) x common factors =1 x 1 = 1

LCM(687,662) = ( 687 × 662 ) / 1

LCM(687,662) = 454794 / 1

LCM(687,662) = 454794

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FAQs on GCF of Fractions of 828/687, 1220/662

1. What is the HCF of 828,1220?

The HCF of 828,1220 is 4

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 828/687, 1220/662?

Answer: GCF of Numerators as per given numbers 828/687, 1220/662 is

GCF of Numerators i.e. for 828,1220 is 4

LCM of denominators i.e. for 687,662 is 454794.

Thus, GCF of Fractions is 4/454794.Finally, GCF of Fractions for 828/687, 1220/662 is 4/454794.