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GCF of 406/59, 122/200

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 406/59, 122/200 i.e 2/11800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 406/59, 122/200.

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 406/59,122/200?

Given fractions are 406/59,122/200

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 406/59,122/200, numerators are 406,122

Denominators are 59,200

The GCF of 406,122 is 2 .

LCM of 59,200 is 11800.

The greatest common factor of 406/59,122/200 = [GCF of 406,122]/[LCM of 59,200]= 2/11800

Therefore, the GCF of 406/59,122/200 is 2/11800.

Greatest Common Factor of 406,122

To find the highest common factor of 406,122, 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 122 are 1, 2, 61, 122

The HCF of 406,122 is 2.

Lets's calculate GCF of 406,122

Greatest Common Factor (GCF) of 406,122 By Common Division

2 406, 122
203, 61

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

Greatest Common Factor of 406,122 By Matching Biggest Common Factor Method

Greatest Common Factor of 406,122 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 122

:

1,2,61,122

Greatest Common Factor

We found the factors 406,122 . The biggest common factor number is the GCF number.
So the greatest common factor 406,122 is 2.

Lets's calculate LCM of 59,200

Lowest Common Multiple of 59,200 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 11800

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11800

Therefore, the GCF of Fractions 406/59,122/200 is 2/11800

Least Common Multiple of 59,200 with GCF Formula

Least Common Multiple of 59,200 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 59,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(59,200) = 1

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

GCF(59,200) x common factors =1 x 1 = 1

LCM(59,200) = ( 59 × 200 ) / 1

LCM(59,200) = 11800 / 1

LCM(59,200) = 11800


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FAQs on GCF of Fractions of 406/59, 122/200

1. What is the HCF of 406,122?

The HCF of 406,122 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 406/59, 122/200?

Answer: GCF of Numerators as per given numbers 406/59, 122/200 is

GCF of Numerators i.e. for 406,122 is 2

LCM of denominators i.e. for 59,200 is 11800.

Thus, GCF of Fractions is 2/11800.Finally, GCF of Fractions for 406/59, 122/200 is 2/11800.