GCF of 62/10, 34/68, 21/51, 78/20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 62/10, 34/68, 21/51, 78/20 i.e 1/1020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 62/10, 34/68, 21/51, 78/20.
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 62/10,34/68,21/51,78/20?
Given fractions are 62/10,34/68,21/51,78/20
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 62/10,34/68,21/51,78/20, numerators are 62,34,21,78
Denominators are 10,68,51,20
The GCF of 62,34,21,78 is 1 .
LCM of 10,68,51,20 is 1020.
The greatest common factor of 62/10,34/68,21/51,78/20 = [GCF of 62,34,21,78]/[LCM of 10,68,51,20]= 1/1020
Therefore, the GCF of 62/10,34/68,21/51,78/20 is 1/1020.
To find the highest common factor of 62,34,21,78, we have to find the factors of both numbers and list the highest common factor.
The factors of 62 are 1, 2, 31, 62
The factors of 34 are 1, 2, 17, 34
The factors of 21 are 1, 3, 7, 21
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
The HCF of 62,34,21,78 is 1.
Lets's calculate GCF of 62,34,21,78
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 62,34,21,78 By Matching Biggest Common Factor Method
Now, list down the factors of 62
:1,2,31,62
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 78
:1,2,3,6,13,26,39,78
Greatest Common Factor
We found the factors 62,34,21,78 . The biggest common factor number is the GCF number.
So the greatest common factor 62,34,21,78 is 1.
Lets's calculate LCM of 10,68,51,20
| 2 | 10, 68, 51, 20 |
| 2 | 5, 34, 51, 10 |
| 5 | 5, 17, 51, 5 |
| 17 | 1, 17, 51, 1 |
| 1, 1, 3, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 17 x 1 x 1 x 3 x 1 = 1020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1020
Therefore, the GCF of Fractions 62/10,34/68,21/51,78/20 is 1/1020
Least Common Multiple of 10,68,51,20 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 10,68,51,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,68,51,20) = 1
common factors(in case of two or more numbers have common factors) = 680
GCF(10,68,51,20) x common factors =1 x 680 = 680
LCM(10,68,51,20) = ( 10 × 68 × 51 × 20 ) / 680
LCM(10,68,51,20) = 693600 / 680
LCM(10,68,51,20) = 1020
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 62/10, 34/68, 21/51, 78/20
1. What is the HCF of 62,34,21,78?
The HCF of 62,34,21,78 is 1
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 62/10, 34/68, 21/51, 78/20?
Answer: GCF of Numerators as per given numbers 62/10, 34/68, 21/51, 78/20 is
GCF of Numerators i.e. for 62,34,21,78 is 1
LCM of denominators i.e. for 10,68,51,20 is 1020.
Thus, GCF of Fractions is 1/1020.Finally, GCF of Fractions for 62/10, 34/68, 21/51, 78/20 is 1/1020.