GCF of 561/70, 530/20, 278/84
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 561/70, 530/20, 278/84 i.e 1/420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 561/70, 530/20, 278/84.
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 561/70,530/20,278/84?
Given fractions are 561/70,530/20,278/84
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 561/70,530/20,278/84, numerators are 561,530,278
Denominators are 70,20,84
The GCF of 561,530,278 is 1 .
LCM of 70,20,84 is 420.
The greatest common factor of 561/70,530/20,278/84 = [GCF of 561,530,278]/[LCM of 70,20,84]= 1/420
Therefore, the GCF of 561/70,530/20,278/84 is 1/420.
To find the highest common factor of 561,530,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561
The factors of 530 are 1, 2, 5, 10, 53, 106, 265, 530
The factors of 278 are 1, 2, 139, 278
The HCF of 561,530,278 is 1.
Lets's calculate GCF of 561,530,278
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 561,530,278 By Matching Biggest Common Factor Method
Now, list down the factors of 561
:1,3,11,17,33,51,187,561
Now, list down the factors of 530
:1,2,5,10,53,106,265,530
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 561,530,278 . The biggest common factor number is the GCF number.
So the greatest common factor 561,530,278 is 1.
Lets's calculate LCM of 70,20,84
| 2 | 70, 20, 84 |
| 2 | 35, 10, 42 |
| 5 | 35, 5, 21 |
| 7 | 7, 1, 21 |
| 1, 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 7 x 1 x 1 x 3 = 420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/420
Therefore, the GCF of Fractions 561/70,530/20,278/84 is 1/420
Least Common Multiple of 70,20,84 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 70,20,84 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(70,20,84) = 2
common factors(in case of two or more numbers have common factors) = 140
GCF(70,20,84) x common factors =2 x 140 = 280
LCM(70,20,84) = ( 70 × 20 × 84 ) / 280
LCM(70,20,84) = 117600 / 280
LCM(70,20,84) = 420
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FAQs on GCF of Fractions of 561/70, 530/20, 278/84
1. What is the HCF of 561,530,278?
The HCF of 561,530,278 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 561/70, 530/20, 278/84?
Answer: GCF of Numerators as per given numbers 561/70, 530/20, 278/84 is
GCF of Numerators i.e. for 561,530,278 is 1
LCM of denominators i.e. for 70,20,84 is 420.
Thus, GCF of Fractions is 1/420.Finally, GCF of Fractions for 561/70, 530/20, 278/84 is 1/420.