GCF of 642/77, 154/412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 642/77, 154/412 i.e 2/31724 easily. The following is the detailed procedure to determine the greatest common factor of fractions 642/77, 154/412.
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 642/77,154/412?
Given fractions are 642/77,154/412
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 642/77,154/412, numerators are 642,154
Denominators are 77,412
The GCF of 642,154 is 2 .
LCM of 77,412 is 31724.
The greatest common factor of 642/77,154/412 = [GCF of 642,154]/[LCM of 77,412]= 2/31724
Therefore, the GCF of 642/77,154/412 is 2/31724.
To find the highest common factor of 642,154, we have to find the factors of both numbers and list the highest common factor.
The factors of 642 are 1, 2, 3, 6, 107, 214, 321, 642
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154
The HCF of 642,154 is 2.
Lets's calculate GCF of 642,154
| 2 | 642, 154 |
| 321, 77 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 642,154 By Matching Biggest Common Factor Method
Now, list down the factors of 642
:1,2,3,6,107,214,321,642
Now, list down the factors of 154
:1,2,7,11,14,22,77,154
Greatest Common Factor
We found the factors 642,154 . The biggest common factor number is the GCF number.
So the greatest common factor 642,154 is 2.
Lets's calculate LCM of 77,412
Given numbers has no common factors except 1. So, there LCM is their product i.e 31724
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/31724
Therefore, the GCF of Fractions 642/77,154/412 is 2/31724
Least Common Multiple of 77,412 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 77,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,412) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,412) x common factors =1 x 1 = 1
LCM(77,412) = ( 77 × 412 ) / 1
LCM(77,412) = 31724 / 1
LCM(77,412) = 31724
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FAQs on GCF of Fractions of 642/77, 154/412
1. What is the HCF of 642,154?
The HCF of 642,154 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 642/77, 154/412?
Answer: GCF of Numerators as per given numbers 642/77, 154/412 is
GCF of Numerators i.e. for 642,154 is 2
LCM of denominators i.e. for 77,412 is 31724.
Thus, GCF of Fractions is 2/31724.Finally, GCF of Fractions for 642/77, 154/412 is 2/31724.