How to Find GCF of 429/589, 616/986?

GCF of 429/589, 616/986

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 429/589, 616/986 i.e 11/580754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 429/589, 616/986.

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 429/589,616/986?

Given fractions are 429/589,616/986

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 429/589,616/986, numerators are 429,616

Denominators are 589,986

The GCF of 429,616 is 11 .

LCM of 589,986 is 580754.

The greatest common factor of 429/589,616/986 = [GCF of 429,616]/[LCM of 589,986]= 11/580754

Therefore, the GCF of 429/589,616/986 is 11/580754.

Greatest Common Factor of 429,616

To find the highest common factor of 429,616, we have to find the factors of both numbers and list the highest common factor.

The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429

The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616

The HCF of 429,616 is 11.

Lets's calculate GCF of 429,616

Greatest Common Factor (GCF) of 429,616 By Common Division

11	429, 616
	39, 56

∴ So the GCF of the given numbers is 11 = 11

Greatest Common Factor of 429,616 By Matching Biggest Common Factor Method

Now, list down the factors of 429

1,3,11,13,33,39,143,429

Now, list down the factors of 616

1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616

Greatest Common Factor

We found the factors 429,616 . The biggest common factor number is the GCF number.
So the greatest common factor 429,616 is 11.

Lets's calculate LCM of 589,986

Lowest Common Multiple of 589,986 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 580754

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/580754

Therefore, the GCF of Fractions 429/589,616/986 is 11/580754

Least Common Multiple of 589,986 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 589,986 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(589,986) = 1

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

GCF(589,986) x common factors =1 x 1 = 1

LCM(589,986) = ( 589 × 986 ) / 1

LCM(589,986) = 580754 / 1

LCM(589,986) = 580754

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FAQs on GCF of Fractions of 429/589, 616/986

1. What is the HCF of 429,616?

The HCF of 429,616 is 11

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 429/589, 616/986?

Answer: GCF of Numerators as per given numbers 429/589, 616/986 is

GCF of Numerators i.e. for 429,616 is 11

LCM of denominators i.e. for 589,986 is 580754.

Thus, GCF of Fractions is 11/580754.Finally, GCF of Fractions for 429/589, 616/986 is 11/580754.