# 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, D:S are with the remainder of 1,
• Plumber The plumber had to cut the metal strip with dimensions 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?
• 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.
• 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. Determine 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)
• 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 to 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?
• 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 we must buy that we can pay in cash only whole euros?
• Diofant 2 Is equation 70x +52y = 34 solvable on the set of integers Z?
• Hectares The tractor plows the first day of 4.5 ha, the second day 6.3 ha, and the third day of 5.4 ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is i The local reader’s club has a set of 28 hardback books and a set of 44 paperbacks. Each set can be divided equally among the club members. What is the greatest possible number of club members? The least common denominator of 2/5, 1/2, and 3/4 Write seven 4-digit numbers that are divisible by 3 and at the same time by 4. A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ] What fraction is 15 of 35 in simplest form?