How to Find GCF of 380/978, 1976/444?

GCF of 380/978, 1976/444

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 380/978, 1976/444 i.e 76/72372 easily. The following is the detailed procedure to determine the greatest common factor of fractions 380/978, 1976/444.

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 380/978,1976/444?

Given fractions are 380/978,1976/444

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 380/978,1976/444, numerators are 380,1976

Denominators are 978,444

The GCF of 380,1976 is 76 .

LCM of 978,444 is 72372.

The greatest common factor of 380/978,1976/444 = [GCF of 380,1976]/[LCM of 978,444]= 76/72372

Therefore, the GCF of 380/978,1976/444 is 76/72372.

Greatest Common Factor of 380,1976

To find the highest common factor of 380,1976, we have to find the factors of both numbers and list the highest common factor.

The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

The factors of 1976 are 1, 2, 4, 8, 13, 19, 26, 38, 52, 76, 104, 152, 247, 494, 988, 1976

The HCF of 380,1976 is 76.

Lets's calculate GCF of 380,1976

Greatest Common Factor (GCF) of 380,1976 By Common Division

2	380, 1976
2	190, 988
19	95, 494
	5, 26

∴ So the GCF of the given numbers is 2 x 2 x 19 = 76

Greatest Common Factor of 380,1976 By Matching Biggest Common Factor Method

Now, list down the factors of 380

1,2,4,5,10,19,20,38,76,95,190,380

Now, list down the factors of 1976

1,2,4,8,13,19,26,38,52,76,104,152,247,494,988,1976

Greatest Common Factor

We found the factors 380,1976 . The biggest common factor number is the GCF number.
So the greatest common factor 380,1976 is 76.

Lets's calculate LCM of 978,444

Lowest Common Multiple of 978,444 using Common Division

2	978, 444
3	489, 222
	163, 74

∴ So the LCM of the given numbers is 2 x 3 x 163 x 74 = 72372

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 76/72372

Therefore, the GCF of Fractions 380/978,1976/444 is 76/72372

Least Common Multiple of 978,444 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 978,444 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,444) = 6

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

GCF(978,444) x common factors =6 x 1 = 6

LCM(978,444) = ( 978 × 444 ) / 6

LCM(978,444) = 434232 / 6

LCM(978,444) = 72372

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 380/978, 1976/444

1. What is the HCF of 380,1976?

The HCF of 380,1976 is 76

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 380/978, 1976/444?

Answer: GCF of Numerators as per given numbers 380/978, 1976/444 is

GCF of Numerators i.e. for 380,1976 is 76

LCM of denominators i.e. for 978,444 is 72372.

Thus, GCF of Fractions is 76/72372.Finally, GCF of Fractions for 380/978, 1976/444 is 76/72372.