GCF of 429/742, 5322/768
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 429/742, 5322/768 i.e 3/284928 easily. The following is the detailed procedure to determine the greatest common factor of fractions 429/742, 5322/768.
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 429/742,5322/768?
Given fractions are 429/742,5322/768
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 429/742,5322/768, numerators are 429,5322
Denominators are 742,768
The GCF of 429,5322 is 3 .
LCM of 742,768 is 284928.
The greatest common factor of 429/742,5322/768 = [GCF of 429,5322]/[LCM of 742,768]= 3/284928
Therefore, the GCF of 429/742,5322/768 is 3/284928.
To find the highest common factor of 429,5322, we have to find the factors of both numbers and list the highest common factor.
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The factors of 5322 are 1, 2, 3, 6, 887, 1774, 2661, 5322
The HCF of 429,5322 is 3.
Lets's calculate GCF of 429,5322
| 3 | 429, 5322 |
| 143, 1774 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 429,5322 By Matching Biggest Common Factor Method
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Now, list down the factors of 5322
:1,2,3,6,887,1774,2661,5322
Greatest Common Factor
We found the factors 429,5322 . The biggest common factor number is the GCF number.
So the greatest common factor 429,5322 is 3.
Lets's calculate LCM of 742,768
| 2 | 742, 768 |
| 371, 384 |
∴ So the LCM of the given numbers is 2 x 371 x 384 = 284928
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/284928
Therefore, the GCF of Fractions 429/742,5322/768 is 3/284928
Least Common Multiple of 742,768 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 742,768 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(742,768) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(742,768) x common factors =2 x 1 = 2
LCM(742,768) = ( 742 × 768 ) / 2
LCM(742,768) = 569856 / 2
LCM(742,768) = 284928
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FAQs on GCF of Fractions of 429/742, 5322/768
1. What is the HCF of 429,5322?
The HCF of 429,5322 is 3
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 429/742, 5322/768?
Answer: GCF of Numerators as per given numbers 429/742, 5322/768 is
GCF of Numerators i.e. for 429,5322 is 3
LCM of denominators i.e. for 742,768 is 284928.
Thus, GCF of Fractions is 3/284928.Finally, GCF of Fractions for 429/742, 5322/768 is 3/284928.