Get help with finding GCF of fractions 75/175, 125/343, 150/490 using GCF of Fractions Calculator to know the result 25/17150 the largest number that divides all the numbers with a zero remainder.

Greatest common factor (GCF) of 75/175, 125/343, 150/490 is **25/17150**.

GCF(75/175, 125/343, 150/490) = 25/17150

Enter two or more fractions separated by **"commas"**

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

Given fractions are 75/175,125/343,150/490

Formula to find GCF of Fractions is

GCF = GCF of Numerators/LCM of Denominators

As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators

In the given fractions GCF of Numerators means GCF of 75,125,150

Greatest Common Factor of Numerators i.e. GCF of 75,125,150 is 25 .

LCM of Denominators means LCM of 175,343,490 as per the given fractions.

LCM of 175,343,490 is 17150 as it is the smallest common factor for both these numbers.

Lets's calculate GCF of 75,125,150

5 | 75, 125, 150 |

5 | 15, 25, 30 |

3, 5, 6 |

∴ So the GCF of the given numbers is 5 x 5 = 25

**Factors of 75**

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

**Factors of 125**

List of positive integer factors of 125 that divides 125 without a remainder.

1,5,25,125

**Factors of 150**

List of positive integer factors of 150 that divides 150 without a remainder.

1,2,3,5,6,10,15,25,30,50,75,150

**Greatest Common Factor**

We found the factors 75,125,150 . The biggest common factor number is the **GCF** number.

So the **greatest common factor 75,125,150 ** is **25**.

Lets's calculate LCM of 175,343,490

5 | 175, 343, 490 |

7 | 35, 343, 98 |

7 | 5, 49, 14 |

5, 7, 2 |

∴ So the LCM of the given numbers is 5 x 7 x 7 x 5 x 7 x 2 = 17150

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/17150

Therefore, the GCF of Fractions 75/175,125/343,150/490 is 25/17150

The formula of **LCM** is LCM(a_{1},a_{2},a_{3}....,a_{n}) = ( a_{1} × a_{2} × a_{3} × .... × a_{n}) / GCF(a_{1},a_{2},a_{3}....,a_{n}) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 175,343,490 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(175,343,490) = 7

common factors(in case of two or more numbers have common factors) = 245

GCF(175,343,490) x common factors =7 x 245 = 1715

LCM(175,343,490) = ( 175 × 343 × 490 ) / 1715

LCM(175,343,490) = 29412250 / 1715

LCM(175,343,490) = 17150

Here are some samples of GCF of Fractions calculations.

1. 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.

2. What is the GCF of Fractions for 75/175, 125/343, 150/490?

Answer: GCF of Numerators as per given numbers 75/175, 125/343, 150/490 is

GCF of Numerators i.e. for 75,125,150 is 25

LCM of denominators i.e. for 175,343,490 is 17150.

Thus, GCF of Fractions is 25/17150.Finally, GCF of Fractions for 75/175, 125/343, 150/490 is 25/17150.