GCF of 429/57, 752/45, 420/10
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 429/57, 752/45, 420/10 i.e 1/1710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 429/57, 752/45, 420/10.
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 429/57,752/45,420/10?
Given fractions are 429/57,752/45,420/10
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 429/57,752/45,420/10, numerators are 429,752,420
Denominators are 57,45,10
The GCF of 429,752,420 is 1 .
LCM of 57,45,10 is 1710.
The greatest common factor of 429/57,752/45,420/10 = [GCF of 429,752,420]/[LCM of 57,45,10]= 1/1710
Therefore, the GCF of 429/57,752/45,420/10 is 1/1710.
To find the highest common factor of 429,752,420, 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 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 429,752,420 is 1.
Lets's calculate GCF of 429,752,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 429,752,420 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 752
:1,2,4,8,16,47,94,188,376,752
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 429,752,420 . The biggest common factor number is the GCF number.
So the greatest common factor 429,752,420 is 1.
Lets's calculate LCM of 57,45,10
| 3 | 57, 45, 10 |
| 5 | 19, 15, 10 |
| 19, 3, 2 |
∴ So the LCM of the given numbers is 3 x 5 x 19 x 3 x 2 = 1710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1710
Therefore, the GCF of Fractions 429/57,752/45,420/10 is 1/1710
Least Common Multiple of 57,45,10 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 57,45,10 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,45,10) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(57,45,10) x common factors =1 x 15 = 15
LCM(57,45,10) = ( 57 × 45 × 10 ) / 15
LCM(57,45,10) = 25650 / 15
LCM(57,45,10) = 1710
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FAQs on GCF of Fractions of 429/57, 752/45, 420/10
1. What is the HCF of 429,752,420?
The HCF of 429,752,420 is 1
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 429/57, 752/45, 420/10?
Answer: GCF of Numerators as per given numbers 429/57, 752/45, 420/10 is
GCF of Numerators i.e. for 429,752,420 is 1
LCM of denominators i.e. for 57,45,10 is 1710.
Thus, GCF of Fractions is 1/1710.Finally, GCF of Fractions for 429/57, 752/45, 420/10 is 1/1710.