How to Find GCF of 874/977, 912/945?

GCF of 874/977, 912/945

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 874/977, 912/945 i.e 38/923265 easily. The following is the detailed procedure to determine the greatest common factor of fractions 874/977, 912/945.

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 874/977,912/945?

Given fractions are 874/977,912/945

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 874/977,912/945, numerators are 874,912

Denominators are 977,945

The GCF of 874,912 is 38 .

LCM of 977,945 is 923265.

The greatest common factor of 874/977,912/945 = [GCF of 874,912]/[LCM of 977,945]= 38/923265

Therefore, the GCF of 874/977,912/945 is 38/923265.

Greatest Common Factor of 874,912

To find the highest common factor of 874,912, we have to find the factors of both numbers and list the highest common factor.

The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874

The factors of 912 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912

The HCF of 874,912 is 38.

Lets's calculate GCF of 874,912

Greatest Common Factor (GCF) of 874,912 By Common Division

2	874, 912
19	437, 456
	23, 24

∴ So the GCF of the given numbers is 2 x 19 = 38

Greatest Common Factor of 874,912 By Matching Biggest Common Factor Method

Now, list down the factors of 874

1,2,19,23,38,46,437,874

Now, list down the factors of 912

1,2,3,4,6,8,12,16,19,24,38,48,57,76,114,152,228,304,456,912

Greatest Common Factor

We found the factors 874,912 . The biggest common factor number is the GCF number.
So the greatest common factor 874,912 is 38.

Lets's calculate LCM of 977,945

Lowest Common Multiple of 977,945 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 923265

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/923265

Therefore, the GCF of Fractions 874/977,912/945 is 38/923265

Least Common Multiple of 977,945 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 977,945 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(977,945) = 1

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

GCF(977,945) x common factors =1 x 1 = 1

LCM(977,945) = ( 977 × 945 ) / 1

LCM(977,945) = 923265 / 1

LCM(977,945) = 923265

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FAQs on GCF of Fractions of 874/977, 912/945

1. What is the HCF of 874,912?

The HCF of 874,912 is 38

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 874/977, 912/945?

Answer: GCF of Numerators as per given numbers 874/977, 912/945 is

GCF of Numerators i.e. for 874,912 is 38

LCM of denominators i.e. for 977,945 is 923265.

Thus, GCF of Fractions is 38/923265.Finally, GCF of Fractions for 874/977, 912/945 is 38/923265.