GCF of 224/66, 840/177
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 224/66, 840/177 i.e 56/3894 easily. The following is the detailed procedure to determine the greatest common factor of fractions 224/66, 840/177.
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 224/66,840/177?
Given fractions are 224/66,840/177
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 224/66,840/177, numerators are 224,840
Denominators are 66,177
The GCF of 224,840 is 56 .
LCM of 66,177 is 3894.
The greatest common factor of 224/66,840/177 = [GCF of 224,840]/[LCM of 66,177]= 56/3894
Therefore, the GCF of 224/66,840/177 is 56/3894.
To find the highest common factor of 224,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 224,840 is 56.
Lets's calculate GCF of 224,840
| 2 | 224, 840 |
| 2 | 112, 420 |
| 2 | 56, 210 |
| 7 | 28, 105 |
| 4, 15 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 7 = 56
Greatest Common Factor of 224,840 By Matching Biggest Common Factor Method
Now, list down the factors of 224
:1,2,4,7,8,14,16,28,32,56,112,224
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 224,840 . The biggest common factor number is the GCF number.
So the greatest common factor 224,840 is 56.
Lets's calculate LCM of 66,177
| 3 | 66, 177 |
| 22, 59 |
∴ So the LCM of the given numbers is 3 x 22 x 59 = 3894
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 56/3894
Therefore, the GCF of Fractions 224/66,840/177 is 56/3894
Least Common Multiple of 66,177 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 66,177 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,177) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(66,177) x common factors =3 x 1 = 3
LCM(66,177) = ( 66 × 177 ) / 3
LCM(66,177) = 11682 / 3
LCM(66,177) = 3894
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FAQs on GCF of Fractions of 224/66, 840/177
1. What is the HCF of 224,840?
The HCF of 224,840 is 56
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 224/66, 840/177?
Answer: GCF of Numerators as per given numbers 224/66, 840/177 is
GCF of Numerators i.e. for 224,840 is 56
LCM of denominators i.e. for 66,177 is 3894.
Thus, GCF of Fractions is 56/3894.Finally, GCF of Fractions for 224/66, 840/177 is 56/3894.