GCF of 16/42, 42/21, 762/667
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 16/42, 42/21, 762/667 i.e 2/28014 easily. The following is the detailed procedure to determine the greatest common factor of fractions 16/42, 42/21, 762/667.
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 16/42,42/21,762/667?
Given fractions are 16/42,42/21,762/667
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 16/42,42/21,762/667, numerators are 16,42,762
Denominators are 42,21,667
The GCF of 16,42,762 is 2 .
LCM of 42,21,667 is 28014.
The greatest common factor of 16/42,42/21,762/667 = [GCF of 16,42,762]/[LCM of 42,21,667]= 2/28014
Therefore, the GCF of 16/42,42/21,762/667 is 2/28014.
To find the highest common factor of 16,42,762, we have to find the factors of both numbers and list the highest common factor.
The factors of 16 are 1, 2, 4, 8, 16
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The HCF of 16,42,762 is 2.
Lets's calculate GCF of 16,42,762
| 2 | 16, 42, 762 |
| 8, 21, 381 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 16,42,762 By Matching Biggest Common Factor Method
Now, list down the factors of 16
:1,2,4,8,16
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Greatest Common Factor
We found the factors 16,42,762 . The biggest common factor number is the GCF number.
So the greatest common factor 16,42,762 is 2.
Lets's calculate LCM of 42,21,667
| 3 | 42, 21, 667 |
| 7 | 14, 7, 667 |
| 2, 1, 667 |
∴ So the LCM of the given numbers is 3 x 7 x 2 x 1 x 667 = 28014
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/28014
Therefore, the GCF of Fractions 16/42,42/21,762/667 is 2/28014
Least Common Multiple of 42,21,667 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 42,21,667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,21,667) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(42,21,667) x common factors =1 x 21 = 21
LCM(42,21,667) = ( 42 × 21 × 667 ) / 21
LCM(42,21,667) = 588294 / 21
LCM(42,21,667) = 28014
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 16/42, 42/21, 762/667
1. What is the HCF of 16,42,762?
The HCF of 16,42,762 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 16/42, 42/21, 762/667?
Answer: GCF of Numerators as per given numbers 16/42, 42/21, 762/667 is
GCF of Numerators i.e. for 16,42,762 is 2
LCM of denominators i.e. for 42,21,667 is 28014.
Thus, GCF of Fractions is 2/28014.Finally, GCF of Fractions for 16/42, 42/21, 762/667 is 2/28014.