How to Find GCF of 154/196, 702/508?

GCF of 154/196, 702/508

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 154/196, 702/508 i.e 2/24892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 154/196, 702/508.

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 154/196,702/508?

Given fractions are 154/196,702/508

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 154/196,702/508, numerators are 154,702

Denominators are 196,508

The GCF of 154,702 is 2 .

LCM of 196,508 is 24892.

The greatest common factor of 154/196,702/508 = [GCF of 154,702]/[LCM of 196,508]= 2/24892

Therefore, the GCF of 154/196,702/508 is 2/24892.

Greatest Common Factor of 154,702

To find the highest common factor of 154,702, 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 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702

The HCF of 154,702 is 2.

Lets's calculate GCF of 154,702

Greatest Common Factor (GCF) of 154,702 By Common Division

2	154, 702
	77, 351

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

Greatest Common Factor of 154,702 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 702

1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702

Greatest Common Factor

We found the factors 154,702 . The biggest common factor number is the GCF number.
So the greatest common factor 154,702 is 2.

Lets's calculate LCM of 196,508

Lowest Common Multiple of 196,508 using Common Division

2	196, 508
2	98, 254
	49, 127

∴ So the LCM of the given numbers is 2 x 2 x 49 x 127 = 24892

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/24892

Therefore, the GCF of Fractions 154/196,702/508 is 2/24892

Least Common Multiple of 196,508 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 196,508 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(196,508) = 4

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

GCF(196,508) x common factors =4 x 1 = 4

LCM(196,508) = ( 196 × 508 ) / 4

LCM(196,508) = 99568 / 4

LCM(196,508) = 24892

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FAQs on GCF of Fractions of 154/196, 702/508

1. What is the HCF of 154,702?

The HCF of 154,702 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 154/196, 702/508?

Answer: GCF of Numerators as per given numbers 154/196, 702/508 is

GCF of Numerators i.e. for 154,702 is 2

LCM of denominators i.e. for 196,508 is 24892.

Thus, GCF of Fractions is 2/24892.Finally, GCF of Fractions for 154/196, 702/508 is 2/24892.