GCF of 61/77, 84/23, 38/42, 80/68
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 61/77, 84/23, 38/42, 80/68 i.e 1/361284 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/77, 84/23, 38/42, 80/68.
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 61/77,84/23,38/42,80/68?
Given fractions are 61/77,84/23,38/42,80/68
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 61/77,84/23,38/42,80/68, numerators are 61,84,38,80
Denominators are 77,23,42,68
The GCF of 61,84,38,80 is 1 .
LCM of 77,23,42,68 is 361284.
The greatest common factor of 61/77,84/23,38/42,80/68 = [GCF of 61,84,38,80]/[LCM of 77,23,42,68]= 1/361284
Therefore, the GCF of 61/77,84/23,38/42,80/68 is 1/361284.
To find the highest common factor of 61,84,38,80, we have to find the factors of both numbers and list the highest common factor.
The factors of 61 are 1, 61
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 38 are 1, 2, 19, 38
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The HCF of 61,84,38,80 is 1.
Lets's calculate GCF of 61,84,38,80
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 61,84,38,80 By Matching Biggest Common Factor Method
Now, list down the factors of 61
:1,61
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Greatest Common Factor
We found the factors 61,84,38,80 . The biggest common factor number is the GCF number.
So the greatest common factor 61,84,38,80 is 1.
Lets's calculate LCM of 77,23,42,68
| 2 | 77, 23, 42, 68 |
| 7 | 77, 23, 21, 34 |
| 11, 23, 3, 34 |
∴ So the LCM of the given numbers is 2 x 7 x 11 x 23 x 3 x 34 = 361284
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/361284
Therefore, the GCF of Fractions 61/77,84/23,38/42,80/68 is 1/361284
Least Common Multiple of 77,23,42,68 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 77,23,42,68 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,23,42,68) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(77,23,42,68) x common factors =1 x 14 = 14
LCM(77,23,42,68) = ( 77 × 23 × 42 × 68 ) / 14
LCM(77,23,42,68) = 5057976 / 14
LCM(77,23,42,68) = 361284
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FAQs on GCF of Fractions of 61/77, 84/23, 38/42, 80/68
1. What is the HCF of 61,84,38,80?
The HCF of 61,84,38,80 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 61/77, 84/23, 38/42, 80/68?
Answer: GCF of Numerators as per given numbers 61/77, 84/23, 38/42, 80/68 is
GCF of Numerators i.e. for 61,84,38,80 is 1
LCM of denominators i.e. for 77,23,42,68 is 361284.
Thus, GCF of Fractions is 1/361284.Finally, GCF of Fractions for 61/77, 84/23, 38/42, 80/68 is 1/361284.