How to Find GCF of 8632/214, 1656/8922?

GCF of 8632/214, 1656/8922

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 8632/214, 1656/8922 i.e 8/954654 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8632/214, 1656/8922.

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 8632/214,1656/8922?

Given fractions are 8632/214,1656/8922

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 8632/214,1656/8922, numerators are 8632,1656

Denominators are 214,8922

The GCF of 8632,1656 is 8 .

LCM of 214,8922 is 954654.

The greatest common factor of 8632/214,1656/8922 = [GCF of 8632,1656]/[LCM of 214,8922]= 8/954654

Therefore, the GCF of 8632/214,1656/8922 is 8/954654.

Greatest Common Factor of 8632,1656

To find the highest common factor of 8632,1656, we have to find the factors of both numbers and list the highest common factor.

The factors of 8632 are 1, 2, 4, 8, 13, 26, 52, 83, 104, 166, 332, 664, 1079, 2158, 4316, 8632

The factors of 1656 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 23, 24, 36, 46, 69, 72, 92, 138, 184, 207, 276, 414, 552, 828, 1656

The HCF of 8632,1656 is 8.

Lets's calculate GCF of 8632,1656

Greatest Common Factor (GCF) of 8632,1656 By Common Division

2	8632, 1656
2	4316, 828
2	2158, 414
	1079, 207

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 8632,1656 By Matching Biggest Common Factor Method

Now, list down the factors of 8632

1,2,4,8,13,26,52,83,104,166,332,664,1079,2158,4316,8632

Now, list down the factors of 1656

1,2,3,4,6,8,9,12,18,23,24,36,46,69,72,92,138,184,207,276,414,552,828,1656

Greatest Common Factor

We found the factors 8632,1656 . The biggest common factor number is the GCF number.
So the greatest common factor 8632,1656 is 8.

Lets's calculate LCM of 214,8922

Lowest Common Multiple of 214,8922 using Common Division

2	214, 8922
	107, 4461

∴ So the LCM of the given numbers is 2 x 107 x 4461 = 954654

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/954654

Therefore, the GCF of Fractions 8632/214,1656/8922 is 8/954654

Least Common Multiple of 214,8922 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 214,8922 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(214,8922) = 2

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

GCF(214,8922) x common factors =2 x 1 = 2

LCM(214,8922) = ( 214 × 8922 ) / 2

LCM(214,8922) = 1909308 / 2

LCM(214,8922) = 954654

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FAQs on GCF of Fractions of 8632/214, 1656/8922

1. What is the HCF of 8632,1656?

The HCF of 8632,1656 is 8

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 8632/214, 1656/8922?

Answer: GCF of Numerators as per given numbers 8632/214, 1656/8922 is

GCF of Numerators i.e. for 8632,1656 is 8

LCM of denominators i.e. for 214,8922 is 954654.

Thus, GCF of Fractions is 8/954654.Finally, GCF of Fractions for 8632/214, 1656/8922 is 8/954654.