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Solved problems for the chapter:

Highest Common Factor (HCF)

View the theory »

The greatest common divisor and the least common multiple

1. Common divisors / factors:

2. Common multiples:

3. Euclidean algorithm:

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:highest_common_factor_%28hcf%29/3926/

Example 1.

Express and as a product of primes factors? What is the Highest Common factor of the two numbers.

Example 2.

Express the numbers , and as the product of prime numbers. Also express the product of these three numbers as the product of prime numbers.

Find five common multiples of numbers and . Start with the smallest.

Determine and

Draw a common diagram of both sets. Specify common factors.
Determines the Highest common factor of both numbers.

Determine , and .

Draw a common set diagram. Determine the common factors of all three numbers.
Determine the highest common factor.

Determine and .

Draw a common diagram of both sets. Specify common factors.
Determines the highest common factor.

We write down the Highest common factor of numbers:

15 and 24
12 and 30
24 and 60
12, 20 and 32
25, 50 and 175

Complete the Equality:

Find:

10.

Express the following numbers as a products of their prime factors and determine the highest common factor:

18, 30
225, 120
1512, 1620

11.

Given the numbers 126 and 224. Find the highest common divisor that is an even number.

12.

Determine the six highest common divisors of 360 and 504.

13.

Given the numbers 270, 450, 675. Write the given numbers as the product of prime numbers and determine the greatest common divisor.

14.

Find the highest common factor of the following pairs using the Euclidean algorithm:

86 and 34
154 and 682
1573 and 7384

15.

Find two numbers whose sum is 104 and their highest common factor is 13.

16.

Determine two natural numbers whose sum is 85 and their least common multiple is 102.

17.

Two men went through the snow from the same point in the same direction. The first has a step 60 cm long and the second 69 cm. How many steps will one and the other take to the city when their degrees coincide again?

18.

A room measuring 570 cm x 420 cm is to be covered with square tiles. What is the maximum possible size of the boards if cutting is not possible?

19.

Determine the highest common factor and the least common multiple of the following expressions:

20.

Determine natural numbers to which the following properties apply:

21.

Find the highest common factor of 50347 and 43183 and express the numbers and as the product of their prime factors.

22.

Given a box measuring 225 mm, 255 mm and 240 mm which needs to be filled with cubes. What is the largest possible dimension of a cube to make this possible?

23.

Determine the greatest common divisor and the least common multiple of the following three terms:

24.

Obtain the smallest and highest prime number that divides 870.

25.

Given that and that

are natural numbers:

Arrange the numbers and in ascending orders, when
. Prove that and are neither prime nor co-prime.
Simplify when .
Calculate the highest common factor and least common multiple of and for .