How to Find GCF of 1956/574, 5312/1567?

GCF of 1956/574, 5312/1567

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 1956/574, 5312/1567 i.e 4/899458 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1956/574, 5312/1567.

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 1956/574,5312/1567?

Given fractions are 1956/574,5312/1567

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 1956/574,5312/1567, numerators are 1956,5312

Denominators are 574,1567

The GCF of 1956,5312 is 4 .

LCM of 574,1567 is 899458.

The greatest common factor of 1956/574,5312/1567 = [GCF of 1956,5312]/[LCM of 574,1567]= 4/899458

Therefore, the GCF of 1956/574,5312/1567 is 4/899458.

Greatest Common Factor of 1956,5312

To find the highest common factor of 1956,5312, we have to find the factors of both numbers and list the highest common factor.

The factors of 1956 are 1, 2, 3, 4, 6, 12, 163, 326, 489, 652, 978, 1956

The factors of 5312 are 1, 2, 4, 8, 16, 32, 64, 83, 166, 332, 664, 1328, 2656, 5312

The HCF of 1956,5312 is 4.

Lets's calculate GCF of 1956,5312

Greatest Common Factor (GCF) of 1956,5312 By Common Division

2	1956, 5312
2	978, 2656
	489, 1328

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 1956,5312 By Matching Biggest Common Factor Method

Now, list down the factors of 1956

1,2,3,4,6,12,163,326,489,652,978,1956

Now, list down the factors of 5312

1,2,4,8,16,32,64,83,166,332,664,1328,2656,5312

Greatest Common Factor

We found the factors 1956,5312 . The biggest common factor number is the GCF number.
So the greatest common factor 1956,5312 is 4.

Lets's calculate LCM of 574,1567

Lowest Common Multiple of 574,1567 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 899458

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/899458

Therefore, the GCF of Fractions 1956/574,5312/1567 is 4/899458

Least Common Multiple of 574,1567 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 574,1567 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(574,1567) = 1

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

GCF(574,1567) x common factors =1 x 1 = 1

LCM(574,1567) = ( 574 × 1567 ) / 1

LCM(574,1567) = 899458 / 1

LCM(574,1567) = 899458

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FAQs on GCF of Fractions of 1956/574, 5312/1567

1. What is the HCF of 1956,5312?

The HCF of 1956,5312 is 4

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 1956/574, 5312/1567?

Answer: GCF of Numerators as per given numbers 1956/574, 5312/1567 is

GCF of Numerators i.e. for 1956,5312 is 4

LCM of denominators i.e. for 574,1567 is 899458.

Thus, GCF of Fractions is 4/899458.Finally, GCF of Fractions for 1956/574, 5312/1567 is 4/899458.