GCF of 771/75, 972/48, 624/12
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 771/75, 972/48, 624/12 i.e 3/1200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 771/75, 972/48, 624/12.
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 771/75,972/48,624/12?
Given fractions are 771/75,972/48,624/12
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 771/75,972/48,624/12, numerators are 771,972,624
Denominators are 75,48,12
The GCF of 771,972,624 is 3 .
LCM of 75,48,12 is 1200.
The greatest common factor of 771/75,972/48,624/12 = [GCF of 771,972,624]/[LCM of 75,48,12]= 3/1200
Therefore, the GCF of 771/75,972/48,624/12 is 3/1200.
To find the highest common factor of 771,972,624, we have to find the factors of both numbers and list the highest common factor.
The factors of 771 are 1, 3, 257, 771
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
The factors of 624 are 1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 104, 156, 208, 312, 624
The HCF of 771,972,624 is 3.
Lets's calculate GCF of 771,972,624
| 3 | 771, 972, 624 |
| 257, 324, 208 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 771,972,624 By Matching Biggest Common Factor Method
Now, list down the factors of 771
:1,3,257,771
Now, list down the factors of 972
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,243,324,486,972
Now, list down the factors of 624
:1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
Greatest Common Factor
We found the factors 771,972,624 . The biggest common factor number is the GCF number.
So the greatest common factor 771,972,624 is 3.
Lets's calculate LCM of 75,48,12
| 2 | 75, 48, 12 |
| 2 | 75, 24, 6 |
| 3 | 75, 12, 3 |
| 25, 4, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 25 x 4 x 1 = 1200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1200
Therefore, the GCF of Fractions 771/75,972/48,624/12 is 3/1200
Least Common Multiple of 75,48,12 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 75,48,12 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,48,12) = 3
common factors(in case of two or more numbers have common factors) = 12
GCF(75,48,12) x common factors =3 x 12 = 36
LCM(75,48,12) = ( 75 × 48 × 12 ) / 36
LCM(75,48,12) = 43200 / 36
LCM(75,48,12) = 1200
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 771/75, 972/48, 624/12
1. What is the HCF of 771,972,624?
The HCF of 771,972,624 is 3
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 771/75, 972/48, 624/12?
Answer: GCF of Numerators as per given numbers 771/75, 972/48, 624/12 is
GCF of Numerators i.e. for 771,972,624 is 3
LCM of denominators i.e. for 75,48,12 is 1200.
Thus, GCF of Fractions is 3/1200.Finally, GCF of Fractions for 771/75, 972/48, 624/12 is 3/1200.