GCF of 68/78, 67/90, 45/30, 56/762
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 68/78, 67/90, 45/30, 56/762 i.e 1/148590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/78, 67/90, 45/30, 56/762.
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 68/78,67/90,45/30,56/762?
Given fractions are 68/78,67/90,45/30,56/762
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 68/78,67/90,45/30,56/762, numerators are 68,67,45,56
Denominators are 78,90,30,762
The GCF of 68,67,45,56 is 1 .
LCM of 78,90,30,762 is 148590.
The greatest common factor of 68/78,67/90,45/30,56/762 = [GCF of 68,67,45,56]/[LCM of 78,90,30,762]= 1/148590
Therefore, the GCF of 68/78,67/90,45/30,56/762 is 1/148590.
To find the highest common factor of 68,67,45,56, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 67 are 1, 67
The factors of 45 are 1, 3, 5, 9, 15, 45
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
The HCF of 68,67,45,56 is 1.
Lets's calculate GCF of 68,67,45,56
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 68,67,45,56 By Matching Biggest Common Factor Method
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 67
:1,67
Now, list down the factors of 45
:1,3,5,9,15,45
Now, list down the factors of 56
:1,2,4,7,8,14,28,56
Greatest Common Factor
We found the factors 68,67,45,56 . The biggest common factor number is the GCF number.
So the greatest common factor 68,67,45,56 is 1.
Lets's calculate LCM of 78,90,30,762
| 2 | 78, 90, 30, 762 |
| 3 | 39, 45, 15, 381 |
| 5 | 13, 5, 15, 127 |
| 13, 1, 3, 127 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 13 x 1 x 3 x 127 = 148590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/148590
Therefore, the GCF of Fractions 68/78,67/90,45/30,56/762 is 1/148590
Least Common Multiple of 78,90,30,762 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 78,90,30,762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,90,30,762) = 6
common factors(in case of two or more numbers have common factors) = 180
GCF(78,90,30,762) x common factors =6 x 180 = 1080
LCM(78,90,30,762) = ( 78 × 90 × 30 × 762 ) / 1080
LCM(78,90,30,762) = 160477200 / 1080
LCM(78,90,30,762) = 148590
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FAQs on GCF of Fractions of 68/78, 67/90, 45/30, 56/762
1. What is the HCF of 68,67,45,56?
The HCF of 68,67,45,56 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 68/78, 67/90, 45/30, 56/762?
Answer: GCF of Numerators as per given numbers 68/78, 67/90, 45/30, 56/762 is
GCF of Numerators i.e. for 68,67,45,56 is 1
LCM of denominators i.e. for 78,90,30,762 is 148590.
Thus, GCF of Fractions is 1/148590.Finally, GCF of Fractions for 68/78, 67/90, 45/30, 56/762 is 1/148590.