GCF of 612/53, 786/782
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 612/53, 786/782 i.e 6/41446 easily. The following is the detailed procedure to determine the greatest common factor of fractions 612/53, 786/782.
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 612/53,786/782?
Given fractions are 612/53,786/782
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 612/53,786/782, numerators are 612,786
Denominators are 53,782
The GCF of 612,786 is 6 .
LCM of 53,782 is 41446.
The greatest common factor of 612/53,786/782 = [GCF of 612,786]/[LCM of 53,782]= 6/41446
Therefore, the GCF of 612/53,786/782 is 6/41446.
To find the highest common factor of 612,786, we have to find the factors of both numbers and list the highest common factor.
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786
The HCF of 612,786 is 6.
Lets's calculate GCF of 612,786
| 2 | 612, 786 |
| 3 | 306, 393 |
| 102, 131 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 612,786 By Matching Biggest Common Factor Method
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Now, list down the factors of 786
:1,2,3,6,131,262,393,786
Greatest Common Factor
We found the factors 612,786 . The biggest common factor number is the GCF number.
So the greatest common factor 612,786 is 6.
Lets's calculate LCM of 53,782
Given numbers has no common factors except 1. So, there LCM is their product i.e 41446
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/41446
Therefore, the GCF of Fractions 612/53,786/782 is 6/41446
Least Common Multiple of 53,782 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 53,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(53,782) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(53,782) x common factors =1 x 1 = 1
LCM(53,782) = ( 53 × 782 ) / 1
LCM(53,782) = 41446 / 1
LCM(53,782) = 41446
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FAQs on GCF of Fractions of 612/53, 786/782
1. What is the HCF of 612,786?
The HCF of 612,786 is 6
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 612/53, 786/782?
Answer: GCF of Numerators as per given numbers 612/53, 786/782 is
GCF of Numerators i.e. for 612,786 is 6
LCM of denominators i.e. for 53,782 is 41446.
Thus, GCF of Fractions is 6/41446.Finally, GCF of Fractions for 612/53, 786/782 is 6/41446.