Divisors

What is Divisor in Math?

Divisor in math is a number that divided another number evenly without leaving any remainder.

How to find Divisors of a Number?

There are 2 main ways to find out the divisors of a number:

1. Take out all the factors of the number i.e 1 and the number itself.
2. Use prime factorization method.

What are Divisors of 12?

• 1 x 12 = 12
• 2 x 6 = 12
• 3 x 4 = 12
• 4 x 3 = 12

Therefore, the divisors of the numbers 12 are 1, 2, 3, 4, and 12

What are 1 digit Divisors?

1 digit or single digit divisors are positive integers that range from 1 – 9 which are divisors of any given number.

What are Divisors of 36?

• 1 x 36 = 36
• 2 x 18 = 36
• 3 x 12 = 36
• 4 x 9 = 36
• 6 x 6 = 36

Therefore, the divisors of the numbers 36 are 1, 2, 3, 4, 6 and 36

What are Common Divisors?

Common divisors are also known as common factors that refers to the positive integers which evenly divided the given numbers without leaving any remainder. 

For example, let’s find the common divisors of 12 and 20

• Divisors of 12: 1, 2, 3, 4, 6 and 12
• Divisors of 24: 1, 2, 4, 5, 10 and 20

Common Divisors of 12 and 20 are 1, 2 and 4

What is a Proper Divisor?

A proper divisor of a number is a divisor other than the number itself. For example, the proper divisors of 12 are 1, 2, 3, 4, and 6.

What is the Greatest Common Divisor (GCD)?

The Greatest Common Divisor (GCD) is the largest positive integer that divides two or more numbers without leaving a remainder. It’s also known as the Greatest Common Factor (GCF).

What is a Perfect Number?

A perfect number is a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6 (1 + 2 + 3 = 6).

What is an Abundant Number?

An abundant number is a positive integer for which the sum of its proper divisors is greater than the number itself. For example, 12 is an abundant number (1 + 2 + 3 + 4 + 6 = 16).

What is a Deficient Number?

A deficient number is a positive integer for which the sum of its proper divisors is less than the number itself. For example, 8 is a deficient number (1 + 2 + 4 = 7).

Can Zero be a Divisor?

No, zero cannot be a divisor. Division by zero is undefined in mathematics.

Divisor is the number from which we divide the dividend to determine the quotient and remainder. In arithmetic, division is one of the four fundamental operations; other operations are addition, subtraction, and multiplication.

Divisors in Number Theory are integers that divides another integer without leaving the remainder is also called a divisor.

In this article, we will discuss both definitions of a divisor, including the general, and the definition in number theory. We will also explore various properties and examples related to divisors and discuss concepts such as prime divisors, the number of divisors, the sum of divisors, and the difference between a divisor and a factor.