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GCF of 306/42, 208/185

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 306/42, 208/185 i.e 2/7770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 306/42, 208/185.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 306/42,208/185?

Given fractions are 306/42,208/185

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 306/42,208/185, numerators are 306,208

Denominators are 42,185

The GCF of 306,208 is 2 .

LCM of 42,185 is 7770.

The greatest common factor of 306/42,208/185 = [GCF of 306,208]/[LCM of 42,185]= 2/7770

Therefore, the GCF of 306/42,208/185 is 2/7770.

Greatest Common Factor of 306,208

To find the highest common factor of 306,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 306,208 is 2.

Lets's calculate GCF of 306,208

Greatest Common Factor (GCF) of 306,208 By Common Division

2 306, 208
153, 104

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

Greatest Common Factor of 306,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 306,208 By Matching Biggest Common Factor Method

Now, list down the factors of 306

:

1,2,3,6,9,17,18,34,51,102,153,306

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 306,208 . The biggest common factor number is the GCF number.
So the greatest common factor 306,208 is 2.

Lets's calculate LCM of 42,185

Lowest Common Multiple of 42,185 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 7770

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7770

Therefore, the GCF of Fractions 306/42,208/185 is 2/7770

Least Common Multiple of 42,185 with GCF Formula

Least Common Multiple of 42,185 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 42,185 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(42,185) = 1

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

GCF(42,185) x common factors =1 x 1 = 1

LCM(42,185) = ( 42 × 185 ) / 1

LCM(42,185) = 7770 / 1

LCM(42,185) = 7770


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FAQs on GCF of Fractions of 306/42, 208/185

1. What is the HCF of 306,208?

The HCF of 306,208 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 306/42, 208/185?

Answer: GCF of Numerators as per given numbers 306/42, 208/185 is

GCF of Numerators i.e. for 306,208 is 2

LCM of denominators i.e. for 42,185 is 7770.

Thus, GCF of Fractions is 2/7770.Finally, GCF of Fractions for 306/42, 208/185 is 2/7770.