GCF of 70/509, 980/123, 614/421
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 70/509, 980/123, 614/421 i.e 2/26357547 easily. The following is the detailed procedure to determine the greatest common factor of fractions 70/509, 980/123, 614/421.
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 70/509,980/123,614/421?
Given fractions are 70/509,980/123,614/421
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 70/509,980/123,614/421, numerators are 70,980,614
Denominators are 509,123,421
The GCF of 70,980,614 is 2 .
LCM of 509,123,421 is 26357547.
The greatest common factor of 70/509,980/123,614/421 = [GCF of 70,980,614]/[LCM of 509,123,421]= 2/26357547
Therefore, the GCF of 70/509,980/123,614/421 is 2/26357547.
To find the highest common factor of 70,980,614, 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 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
The factors of 614 are 1, 2, 307, 614
The HCF of 70,980,614 is 2.
Lets's calculate GCF of 70,980,614
| 2 | 70, 980, 614 |
| 35, 490, 307 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 70,980,614 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 980
:1,2,4,5,7,10,14,20,28,35,49,70,98,140,196,245,490,980
Now, list down the factors of 614
:1,2,307,614
Greatest Common Factor
We found the factors 70,980,614 . The biggest common factor number is the GCF number.
So the greatest common factor 70,980,614 is 2.
Lets's calculate LCM of 509,123,421
Given numbers has no common factors except 1. So, there LCM is their product i.e 26357547
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/26357547
Therefore, the GCF of Fractions 70/509,980/123,614/421 is 2/26357547
Least Common Multiple of 509,123,421 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 509,123,421 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,123,421) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(509,123,421) x common factors =1 x 1 = 1
LCM(509,123,421) = ( 509 × 123 × 421 ) / 1
LCM(509,123,421) = 26357547 / 1
LCM(509,123,421) = 26357547
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FAQs on GCF of Fractions of 70/509, 980/123, 614/421
1. What is the HCF of 70,980,614?
The HCF of 70,980,614 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 70/509, 980/123, 614/421?
Answer: GCF of Numerators as per given numbers 70/509, 980/123, 614/421 is
GCF of Numerators i.e. for 70,980,614 is 2
LCM of denominators i.e. for 509,123,421 is 26357547.
Thus, GCF of Fractions is 2/26357547.Finally, GCF of Fractions for 70/509, 980/123, 614/421 is 2/26357547.