How to Find GCF of 176/978, 6076/274?

GCF of 176/978, 6076/274

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 176/978, 6076/274 i.e 4/133986 easily. The following is the detailed procedure to determine the greatest common factor of fractions 176/978, 6076/274.

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 176/978,6076/274?

Given fractions are 176/978,6076/274

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 176/978,6076/274, numerators are 176,6076

Denominators are 978,274

The GCF of 176,6076 is 4 .

LCM of 978,274 is 133986.

The greatest common factor of 176/978,6076/274 = [GCF of 176,6076]/[LCM of 978,274]= 4/133986

Therefore, the GCF of 176/978,6076/274 is 4/133986.

Greatest Common Factor of 176,6076

To find the highest common factor of 176,6076, we have to find the factors of both numbers and list the highest common factor.

The factors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88, 176

The factors of 6076 are 1, 2, 4, 7, 14, 28, 31, 49, 62, 98, 124, 196, 217, 434, 868, 1519, 3038, 6076

The HCF of 176,6076 is 4.

Lets's calculate GCF of 176,6076

Greatest Common Factor (GCF) of 176,6076 By Common Division

2	176, 6076
2	88, 3038
	44, 1519

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

Greatest Common Factor of 176,6076 By Matching Biggest Common Factor Method

Now, list down the factors of 176

1,2,4,8,11,16,22,44,88,176

Now, list down the factors of 6076

1,2,4,7,14,28,31,49,62,98,124,196,217,434,868,1519,3038,6076

Greatest Common Factor

We found the factors 176,6076 . The biggest common factor number is the GCF number.
So the greatest common factor 176,6076 is 4.

Lets's calculate LCM of 978,274

Lowest Common Multiple of 978,274 using Common Division

2	978, 274
	489, 137

∴ So the LCM of the given numbers is 2 x 489 x 137 = 133986

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/133986

Therefore, the GCF of Fractions 176/978,6076/274 is 4/133986

Least Common Multiple of 978,274 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 978,274 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,274) = 2

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

GCF(978,274) x common factors =2 x 1 = 2

LCM(978,274) = ( 978 × 274 ) / 2

LCM(978,274) = 267972 / 2

LCM(978,274) = 133986

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 176/978, 6076/274

1. What is the HCF of 176,6076?

The HCF of 176,6076 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 176/978, 6076/274?

Answer: GCF of Numerators as per given numbers 176/978, 6076/274 is

GCF of Numerators i.e. for 176,6076 is 4

LCM of denominators i.e. for 978,274 is 133986.

Thus, GCF of Fractions is 4/133986.Finally, GCF of Fractions for 176/978, 6076/274 is 4/133986.