Problems and Solutions

Go through the given number theory problems once to get a better understanding.

Problem 1: Find the Greatest Common Divisor(G.C.D ) of a number 30 and 52

Solution:

Divisors of 30 are 1, 2, 3, 5, 6, 10, 15, 30

Divisors of 52 are 1, 2, 4, 13, 26, 52

The common divisors in 30 and 52 is 2

Therefore, the G. C.D of 30 and 52 is 2

gcd(30,52)= 2

Problem 2: Find the common factors of 10 and 16

Solution:

Factors of 10 are:

2 x 5 =10

1 x 10 = 10

Therefore, the factors are 1, 2, 5 and 10

Factors of 16 are

4 x 4 = 16

1 x 16 = 16

2 x 8 = 16

Therefore, the factors of 16 are as follows: 1, 2, 4, 8, 16

Then, the common factors are 1 and 2.

Problem 3: Show that the greatest factor of a number is the number itself.

Solution:

Assume the number 24

The factors of 24 are

1 x 24 =24

12 x 2 = 24

8 x 3 = 24

6 x 4 = 24

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

From this, we can say that 24 is the greatest factor of a number 24.