Introduction to positive divisors

In math divisor is defined as “the number that you are going to divide by”. Divisor of a given integer can also be called as the divisor of a given integer.

Dividend /Divisor = Quotient.

Positive number/ Negative number = negative number

Negative number/Positive number = negative number

Positive/Positive  = Positive

Let us have an example 16/2 = 8 here 2 is a divisor.

16/4= 4 here 4 is a divisor.

16/8= 2 here 4 is a divisor.

In the above shown example the divisors are positive and also known as positive divisors.

The positive divisors when the dividend is 16 are 8, 4, and 2.

Example Problems for Positive Divisors:

Example problem 1:

Find the positive divisors of 28

Solution:

Positive Divisors of 28 are 1, 2, 4, 7, 14, and 28

Where 28 /1 = 28.

28 /2 = 14.

28 /4 = 7.

28 /7 = 4.

28 /14 = 2.

28 / 28 = 1

Hence for 28 we have 6  Positive divisors

Moreover 28 is a composite number

Example problem 2:

Find the positive divisors of 52

Solution

Positive   Divisors of 52 are 1, 2, 4, 13, 26, and 52.

Where 52/1=52.

52/2=26.

52/4=13.

52/13=4.

52/26=2.

52/52=1.

Hence for 52 we have 6   Positive divisors

Example problem 3:

Find the positive divisors of 30

Solution

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

Where 30/1=30

30/2= 15.

30/3=10.

30/5=4.

30/6=5.

30/10=3.

30/15=2.

30/30=1

Hence for 30 we have 8 Positive divisors

Example problem 4:

Find the positive divisors of 100

Solution

The positive divisors of  100 are  1,2,4,5,10,20,25,50,100

Where 100/1=100

100/2= 50.

100/4=25.

100/5=20.

100/10=10.

100/20=5.

100/25=4.

100/50=2.

100/100=1.

Hence for 100 we have 9 Positive divisors

Example problem 5:

Find the positive divisor of 31

Solution

Given that 31 is a prime number

All the prime numbers have only two divisors

The two divisors are 1 and the numbers itself

So the positive divisor of the number 31 is 1, 31 alone.

Finally the divisors of the prime numbers are 1 and the number itself.

Practice Problems for Positive Divisors:

Problem 1:

Find the positive divisor of 63

Solution:

The divisors of 63 is 1, 3,7,9,21,63

So the number 63 has 6 divisors.

Problem 2:

Find the positive divisor of 37

Solution:

The divisors of 37 are 1, 37

Problem 3:

Find the positive divisor of 15

Solution:

The divisors of 15 is 1, 3, 5, 15

Problem 4:

Find the positive divisor of 35

Solution:

The divisors of 35 is 1, 5, 7, 35