GCF of 429/506, 286/782
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 429/506, 286/782 i.e 143/8602 easily. The following is the detailed procedure to determine the greatest common factor of fractions 429/506, 286/782.
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 429/506,286/782?
Given fractions are 429/506,286/782
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 429/506,286/782, numerators are 429,286
Denominators are 506,782
The GCF of 429,286 is 143 .
LCM of 506,782 is 8602.
The greatest common factor of 429/506,286/782 = [GCF of 429,286]/[LCM of 506,782]= 143/8602
Therefore, the GCF of 429/506,286/782 is 143/8602.
To find the highest common factor of 429,286, 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 286 are 1, 2, 11, 13, 22, 26, 143, 286
The HCF of 429,286 is 143.
Lets's calculate GCF of 429,286
| 11 | 429, 286 |
| 13 | 39, 26 |
| 3, 2 |
∴ So the GCF of the given numbers is 11 x 13 = 143
Greatest Common Factor of 429,286 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 286
:1,2,11,13,22,26,143,286
Greatest Common Factor
We found the factors 429,286 . The biggest common factor number is the GCF number.
So the greatest common factor 429,286 is 143.
Lets's calculate LCM of 506,782
| 2 | 506, 782 |
| 23 | 253, 391 |
| 11, 17 |
∴ So the LCM of the given numbers is 2 x 23 x 11 x 17 = 8602
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 143/8602
Therefore, the GCF of Fractions 429/506,286/782 is 143/8602
Least Common Multiple of 506,782 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 506,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(506,782) = 46
common factors(in case of two or more numbers have common factors) = 1
GCF(506,782) x common factors =46 x 1 = 46
LCM(506,782) = ( 506 × 782 ) / 46
LCM(506,782) = 395692 / 46
LCM(506,782) = 8602
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FAQs on GCF of Fractions of 429/506, 286/782
1. What is the HCF of 429,286?
The HCF of 429,286 is 143
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 429/506, 286/782?
Answer: GCF of Numerators as per given numbers 429/506, 286/782 is
GCF of Numerators i.e. for 429,286 is 143
LCM of denominators i.e. for 506,782 is 8602.
Thus, GCF of Fractions is 143/8602.Finally, GCF of Fractions for 429/506, 286/782 is 143/8602.