GCF of 70/205, 29/514, 762/574
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/205, 29/514, 762/574 i.e 1/737590 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/205, 29/514, 762/574.
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 70/205,29/514,762/574?
Given fractions are 70/205,29/514,762/574
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 70/205,29/514,762/574, numerators are 70,29,762
Denominators are 205,514,574
The GCF of 70,29,762 is 1 .
LCM of 205,514,574 is 737590.
The greatest common factor of 70/205,29/514,762/574 = [GCF of 70,29,762]/[LCM of 205,514,574]= 1/737590
Therefore, the GCF of 70/205,29/514,762/574 is 1/737590.
To find the highest common factor of 70,29,762, we have to find the factors of both numbers and list the highest common factor.
The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
The factors of 29 are 1, 29
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The HCF of 70,29,762 is 1.
Lets's calculate GCF of 70,29,762
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 70,29,762 By Matching Biggest Common Factor Method
Now, list down the factors of 70
:1,2,5,7,10,14,35,70
Now, list down the factors of 29
:1,29
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Greatest Common Factor
We found the factors 70,29,762 . The biggest common factor number is the GCF number.
So the greatest common factor 70,29,762 is 1.
Lets's calculate LCM of 205,514,574
| 2 | 205, 514, 574 |
| 41 | 205, 257, 287 |
| 5, 257, 7 |
∴ So the LCM of the given numbers is 2 x 41 x 5 x 257 x 7 = 737590
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/737590
Therefore, the GCF of Fractions 70/205,29/514,762/574 is 1/737590
Least Common Multiple of 205,514,574 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 205,514,574 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,514,574) = 1
common factors(in case of two or more numbers have common factors) = 82
GCF(205,514,574) x common factors =1 x 82 = 82
LCM(205,514,574) = ( 205 × 514 × 574 ) / 82
LCM(205,514,574) = 60482380 / 82
LCM(205,514,574) = 737590
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FAQs on GCF of Fractions of 70/205, 29/514, 762/574
1. What is the HCF of 70,29,762?
The HCF of 70,29,762 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 70/205, 29/514, 762/574?
Answer: GCF of Numerators as per given numbers 70/205, 29/514, 762/574 is
GCF of Numerators i.e. for 70,29,762 is 1
LCM of denominators i.e. for 205,514,574 is 737590.
Thus, GCF of Fractions is 1/737590.Finally, GCF of Fractions for 70/205, 29/514, 762/574 is 1/737590.