Greatest Common Divisor (GCD) Calculator
GCD(21000, 100) = 22×52 = 100
Calculation
1. Find the prime factorization of each number.2. Find the smallest (common) exponent of each prime factor.
3. Multiply all the prime factors from step 2 together to get the final result.
4. If no prime factors are common to all numbers, the GCD is 1.
21000 = 23×3×53×7
100 = 22×52
GCD = 22×52 = 100
Division by the greatest common divisor
21000 / 100 = 210
100 / 100 = 1
What is GCD?
The greatest common divisor (gcd/GCD), or 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.
Questions and word problems involving GCD
- Gcd and lcm
Calculate the greatest common divisor and the least common multiple of numbers. a) 16 and 18 b) 24 and 22 c) 45 and 60 d) 36 and 30 - Adela number
Adela had two numbers written on the paper. When she added their greatest common divisor and least common multiple, she was given four different numbers less than 100. She was amazed that if she divided the largest of these four numbers by the least, she - Leftovers from boards
The carpenter has three boards 360 cm, 27 dm and 450 cm long, and he wants to cut them into boards of the same length so that there are no leftovers. What will the board be to make it as long as possible? - Rectangular meadow
Divide the rectangular meadow with dimensions of 1280 m and 320 m into a square shepherd with the longest possible side of the square. How many square pastures did you divide the meadow? - Wide field
The field is 203 meters wide and 319 meters long. What is the greater length of the rope by which length and width can be measured? Find the exact number of times. - Largest squares
How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm? - In a forest meadow
The students planted 280 spruces and 60 pines on forest plots. Express the ratio of the number of planted pines to the number of planted spruces as the smallest possible natural numbers. - Cubes
Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes. - Profitable company
Three businessmen decide to open up their own company. They agree to distribute the yearly profits made in the same ratio as their initial investments. They invest R 50 000, R 75 000, and R25 000, respectively. The profit made by the company in the first - LCD 2
The least common denominator of 2/5, 1/2, and 3/4 - Birthdate
Jane brought 30 lollipops and 24 chewing gum for their friends on her birthday. How many friends does she have if everyone receives the same number of lollipops and pieces of chewing gum? How much chewing gum and lollipops have any friends? - Tissues
The store got three kinds of tissues - 132 children, 156 women, and 204 men. Tissues for each species were packed into boxes after the number of pieces was the same for all three types (and greatest). Determine the number if you know that every box has mo - Rectangular flowerbed
Around the rectangular flowerbed with dimensions of 5.25 m and 3.50 m, roses should be planted at the same distance from each other so that they are located in each corner of the flower bed and consumed as little as possible. How far do we plant them? How - Difference GCD - LCM
Calculate the difference between the greatest common divisor and the least common multiple of 24 and 36. - Athletics team
All athletes in an athletics club can be divided evenly into groups of four, five, six, or seven, with no one left over. What is the average number of athletes per group if there are twelve groups in the section? Use the smallest possible total number of
more math problems »
