How to Find GCF of 38/30, 262/78, 974/814?

GCF of 38/30, 262/78, 974/814

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 38/30, 262/78, 974/814 i.e 2/158730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/30, 262/78, 974/814.

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 38/30,262/78,974/814?

Given fractions are 38/30,262/78,974/814

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 38/30,262/78,974/814, numerators are 38,262,974

Denominators are 30,78,814

The GCF of 38,262,974 is 2 .

LCM of 30,78,814 is 158730.

The greatest common factor of 38/30,262/78,974/814 = [GCF of 38,262,974]/[LCM of 30,78,814]= 2/158730

Therefore, the GCF of 38/30,262/78,974/814 is 2/158730.

Greatest Common Factor of 38,262,974

To find the highest common factor of 38,262,974, we have to find the factors of both numbers and list the highest common factor.

The factors of 38 are 1, 2, 19, 38

The factors of 262 are 1, 2, 131, 262

The factors of 974 are 1, 2, 487, 974

The HCF of 38,262,974 is 2.

Lets's calculate GCF of 38,262,974

Greatest Common Factor (GCF) of 38,262,974 By Common Division

2	38, 262, 974
	19, 131, 487

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

Greatest Common Factor of 38,262,974 By Matching Biggest Common Factor Method

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 262

1,2,131,262

Now, list down the factors of 974

1,2,487,974

Greatest Common Factor

We found the factors 38,262,974 . The biggest common factor number is the GCF number.
So the greatest common factor 38,262,974 is 2.

Lets's calculate LCM of 30,78,814

Lowest Common Multiple of 30,78,814 using Common Division

2	30, 78, 814
3	15, 39, 407
	5, 13, 407

∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 407 = 158730

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/158730

Therefore, the GCF of Fractions 38/30,262/78,974/814 is 2/158730

Least Common Multiple of 30,78,814 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 30,78,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,78,814) = 2

common factors(in case of two or more numbers have common factors) = 6

GCF(30,78,814) x common factors =2 x 6 = 12

LCM(30,78,814) = ( 30 × 78 × 814 ) / 12

LCM(30,78,814) = 1904760 / 12

LCM(30,78,814) = 158730

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 38/30, 262/78, 974/814

1. What is the HCF of 38,262,974?

The HCF of 38,262,974 is 2

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 38/30, 262/78, 974/814?

Answer: GCF of Numerators as per given numbers 38/30, 262/78, 974/814 is

GCF of Numerators i.e. for 38,262,974 is 2

LCM of denominators i.e. for 30,78,814 is 158730.

Thus, GCF of Fractions is 2/158730.Finally, GCF of Fractions for 38/30, 262/78, 974/814 is 2/158730.