# Greatest common factor calculator

### What is GCF?

The greatest common factor (gcf), or highest common factor (hcf), of two or more integers (at least one of which is not zero), is the largest positive integer that divides the numbers without a remainder. It is the highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions. The greatest common factor is useful for reducing fractions to be in lowest terms.

## Questions and word problems to GCF

- Reminder and quotient

There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S and D:S are with the remainder of 1. - Plumber

The plumber had to cut the metal strip with dimensions of 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it? - Granddaughter 2789

Grandma and her granddaughter Barunka have a birthday on the same day. During six consecutive birthday celebrations, Grandma's age was always divisible by Barunka's age. How many birthdays did Grandma celebrate at the last of these six celebrations? Grand - Decompose 3076

Decompose into primes and find the greatest divisor of the pair of numbers D (84.70). - On Children's

On Children's Day, the organizers bought 252 chewing gums, 396 candies, and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way. - Determine 8611

Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product. - The classroom

The classroom is 9 meters long. The width of the classroom is smaller and can be passed in equally long steps of 55 CM or 70 CM. Find the width of the classroom. - Decompose

Decompose into primes and find the smallest common multiple n of (16,20) and the largest common divisor D of the pair of numbers (140,100) - Matemakak 9432

The cookbook by Matěj Matemakak says: The greatest common divisor of flour weight and sugar weight is 15, the greatest common divisor of sugar weight and lemon peel weight is 6, the product of sugar weight and lemon peel weight is 1800, and the smallest c - Mathematics 6522

There are more than 20 but less than 40 students in the class. A third of the pupils wrote the mathematics test with a one, a sixth with a two, and a ninth with a three. Nobody got a four. How many students in the class wrote the test on a five? - MO C–I–1 2018

An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Children's home

The children's home received a gift from Nicholas of 54 oranges, 81 chocolate figurines, and 135 apples. Every child received the same gift, and nothing was left. a) How many packages could be prepared? b) what did the children find in the package? - Lcm and hcf

If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a = … - Diofant equation

In the set of integers (Z), solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Seedcake

Seedcake costs 44 cents. How many minimum seedcakes must we buy that we can pay in cash, only whole euros? - Diofant 2

Is equation 70x +52y = 34 solvable on the set of integers Z?

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