How to Find GCF of 154/766, 2574/974?

GCF of 154/766, 2574/974

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 154/766, 2574/974 i.e 22/373042 easily. The following is the detailed procedure to determine the greatest common factor of fractions 154/766, 2574/974.

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 154/766,2574/974?

Given fractions are 154/766,2574/974

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 154/766,2574/974, numerators are 154,2574

Denominators are 766,974

The GCF of 154,2574 is 22 .

LCM of 766,974 is 373042.

The greatest common factor of 154/766,2574/974 = [GCF of 154,2574]/[LCM of 766,974]= 22/373042

Therefore, the GCF of 154/766,2574/974 is 22/373042.

Greatest Common Factor of 154,2574

To find the highest common factor of 154,2574, we have to find the factors of both numbers and list the highest common factor.

The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154

The factors of 2574 are 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 143, 198, 234, 286, 429, 858, 1287, 2574

The HCF of 154,2574 is 22.

Lets's calculate GCF of 154,2574

Greatest Common Factor (GCF) of 154,2574 By Common Division

2	154, 2574
11	77, 1287
	7, 117

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 154,2574 By Matching Biggest Common Factor Method

Now, list down the factors of 154

1,2,7,11,14,22,77,154

Now, list down the factors of 2574

1,2,3,6,9,11,13,18,22,26,33,39,66,78,99,117,143,198,234,286,429,858,1287,2574

Greatest Common Factor

We found the factors 154,2574 . The biggest common factor number is the GCF number.
So the greatest common factor 154,2574 is 22.

Lets's calculate LCM of 766,974

Lowest Common Multiple of 766,974 using Common Division

2	766, 974
	383, 487

∴ So the LCM of the given numbers is 2 x 383 x 487 = 373042

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/373042

Therefore, the GCF of Fractions 154/766,2574/974 is 22/373042

Least Common Multiple of 766,974 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 766,974 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(766,974) = 2

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

GCF(766,974) x common factors =2 x 1 = 2

LCM(766,974) = ( 766 × 974 ) / 2

LCM(766,974) = 746084 / 2

LCM(766,974) = 373042

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 154/766, 2574/974

1. What is the HCF of 154,2574?

The HCF of 154,2574 is 22

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 154/766, 2574/974?

Answer: GCF of Numerators as per given numbers 154/766, 2574/974 is

GCF of Numerators i.e. for 154,2574 is 22

LCM of denominators i.e. for 766,974 is 373042.

Thus, GCF of Fractions is 22/373042.Finally, GCF of Fractions for 154/766, 2574/974 is 22/373042.