GCF of 4/68, 84/77, 32/803, 278/857
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4/68, 84/77, 32/803, 278/857 i.e 2/327569396 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4/68, 84/77, 32/803, 278/857.
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 4/68,84/77,32/803,278/857?
Given fractions are 4/68,84/77,32/803,278/857
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 4/68,84/77,32/803,278/857, numerators are 4,84,32,278
Denominators are 68,77,803,857
The GCF of 4,84,32,278 is 2 .
LCM of 68,77,803,857 is 327569396.
The greatest common factor of 4/68,84/77,32/803,278/857 = [GCF of 4,84,32,278]/[LCM of 68,77,803,857]= 2/327569396
Therefore, the GCF of 4/68,84/77,32/803,278/857 is 2/327569396.
To find the highest common factor of 4,84,32,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 4 are 1, 2, 4
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 278 are 1, 2, 139, 278
The HCF of 4,84,32,278 is 2.
Lets's calculate GCF of 4,84,32,278
| 2 | 4, 84, 32, 278 |
| 2, 42, 16, 139 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 4,84,32,278 By Matching Biggest Common Factor Method
Now, list down the factors of 4
:1,2,4
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 32
:1,2,4,8,16,32
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 4,84,32,278 . The biggest common factor number is the GCF number.
So the greatest common factor 4,84,32,278 is 2.
Lets's calculate LCM of 68,77,803,857
| 11 | 68, 77, 803, 857 |
| 68, 7, 73, 857 |
∴ So the LCM of the given numbers is 11 x 68 x 7 x 73 x 857 = 327569396
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/327569396
Therefore, the GCF of Fractions 4/68,84/77,32/803,278/857 is 2/327569396
Least Common Multiple of 68,77,803,857 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 68,77,803,857 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,77,803,857) = 1
common factors(in case of two or more numbers have common factors) = 11
GCF(68,77,803,857) x common factors =1 x 11 = 11
LCM(68,77,803,857) = ( 68 × 77 × 803 × 857 ) / 11
LCM(68,77,803,857) = 3603263356 / 11
LCM(68,77,803,857) = 327569396
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 4/68, 84/77, 32/803, 278/857
1. What is the HCF of 4,84,32,278?
The HCF of 4,84,32,278 is 2
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 4/68, 84/77, 32/803, 278/857?
Answer: GCF of Numerators as per given numbers 4/68, 84/77, 32/803, 278/857 is
GCF of Numerators i.e. for 4,84,32,278 is 2
LCM of denominators i.e. for 68,77,803,857 is 327569396.
Thus, GCF of Fractions is 2/327569396.Finally, GCF of Fractions for 4/68, 84/77, 32/803, 278/857 is 2/327569396.