GCF of 692/32, 642/8078
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 692/32, 642/8078 i.e 2/129248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 692/32, 642/8078.
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 692/32,642/8078?
Given fractions are 692/32,642/8078
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 692/32,642/8078, numerators are 692,642
Denominators are 32,8078
The GCF of 692,642 is 2 .
LCM of 32,8078 is 129248.
The greatest common factor of 692/32,642/8078 = [GCF of 692,642]/[LCM of 32,8078]= 2/129248
Therefore, the GCF of 692/32,642/8078 is 2/129248.
To find the highest common factor of 692,642, we have to find the factors of both numbers and list the highest common factor.
The factors of 692 are 1, 2, 4, 173, 346, 692
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The HCF of 692,642 is 2.
Lets's calculate GCF of 692,642
| 2 | 692, 642 |
| 346, 321 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 692,642 By Matching Biggest Common Factor Method
Now, list down the factors of 692
:1,2,4,173,346,692
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Greatest Common Factor
We found the factors 692,642 . The biggest common factor number is the GCF number.
So the greatest common factor 692,642 is 2.
Lets's calculate LCM of 32,8078
| 2 | 32, 8078 |
| 16, 4039 |
∴ So the LCM of the given numbers is 2 x 16 x 4039 = 129248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/129248
Therefore, the GCF of Fractions 692/32,642/8078 is 2/129248
Least Common Multiple of 32,8078 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 32,8078 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,8078) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(32,8078) x common factors =2 x 1 = 2
LCM(32,8078) = ( 32 × 8078 ) / 2
LCM(32,8078) = 258496 / 2
LCM(32,8078) = 129248
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FAQs on GCF of Fractions of 692/32, 642/8078
1. What is the HCF of 692,642?
The HCF of 692,642 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 692/32, 642/8078?
Answer: GCF of Numerators as per given numbers 692/32, 642/8078 is
GCF of Numerators i.e. for 692,642 is 2
LCM of denominators i.e. for 32,8078 is 129248.
Thus, GCF of Fractions is 2/129248.Finally, GCF of Fractions for 692/32, 642/8078 is 2/129248.