How to Find GCF of 406/356, 304/964?

GCF of 406/356, 304/964

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 406/356, 304/964 i.e 2/85796 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/356, 304/964.

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 406/356,304/964?

Given fractions are 406/356,304/964

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 406/356,304/964, numerators are 406,304

Denominators are 356,964

The GCF of 406,304 is 2 .

LCM of 356,964 is 85796.

The greatest common factor of 406/356,304/964 = [GCF of 406,304]/[LCM of 356,964]= 2/85796

Therefore, the GCF of 406/356,304/964 is 2/85796.

Greatest Common Factor of 406,304

To find the highest common factor of 406,304, we have to find the factors of both numbers and list the highest common factor.

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304

The HCF of 406,304 is 2.

Lets's calculate GCF of 406,304

Greatest Common Factor (GCF) of 406,304 By Common Division

2	406, 304
	203, 152

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

Greatest Common Factor of 406,304 By Matching Biggest Common Factor Method

Now, list down the factors of 406

1,2,7,14,29,58,203,406

Now, list down the factors of 304

1,2,4,8,16,19,38,76,152,304

Greatest Common Factor

We found the factors 406,304 . The biggest common factor number is the GCF number.
So the greatest common factor 406,304 is 2.

Lets's calculate LCM of 356,964

Lowest Common Multiple of 356,964 using Common Division

2	356, 964
2	178, 482
	89, 241

∴ So the LCM of the given numbers is 2 x 2 x 89 x 241 = 85796

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/85796

Therefore, the GCF of Fractions 406/356,304/964 is 2/85796

Least Common Multiple of 356,964 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 356,964 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(356,964) = 4

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

GCF(356,964) x common factors =4 x 1 = 4

LCM(356,964) = ( 356 × 964 ) / 4

LCM(356,964) = 343184 / 4

LCM(356,964) = 85796

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FAQs on GCF of Fractions of 406/356, 304/964

1. What is the HCF of 406,304?

The HCF of 406,304 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 406/356, 304/964?

Answer: GCF of Numerators as per given numbers 406/356, 304/964 is

GCF of Numerators i.e. for 406,304 is 2

LCM of denominators i.e. for 356,964 is 85796.

Thus, GCF of Fractions is 2/85796.Finally, GCF of Fractions for 406/356, 304/964 is 2/85796.