What are Prime Divisors?
Prime divisors are prime integers (whole numbers) that divide a given integer leaving no remainder. A prime divisor has at least two factors i.e 1 and itself. Below are some examples of prime divisors:
- Prime divisors of 14 are 2 and 7.
- Prime divisors of 18 are 2 and 3.
- Prime divisors of 30 are 2 and 3.
- Prime divisors of 49 are 7.
- Prime divisors of 60 are 2, 3, and 5.
- Prime divisors of 72 are 2 and 3.
- Prime divisors of 91 are 7 and 13.
- Prime divisors of 100 are 2 and 5.
- Prime divisors of 121 are 11.
Prime Divisors of 144
Let’s learn how to calculate prime divisors of number 144 using prime factorization method.
Step 1: Take the number 144 and and divide it with the smallest prime factor 2
- 144 ÷ 2 = 72
Step 2: Again divide 72 by the smallest prime factor 2 as 72 is divisible by 2 and continue the process
- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
Step 3: Now, 9 is not completely divisible by 2 as it will give a fractional number. Let’s divide it with the next smallest prime factor 3
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
Thus, we have a remainder 1. We cannot proceed further.
So, the prime divisors of number 144 are 2 × 2 × 2 × 2 × 3 × 3 or 24 × 32
Prime and Composite Divisors
Prime divisors are prime integers (whole numbers) that divide a given integer leaving no remainder. A prime divisor has at least two factors i.e 1 and itself.
Example: Let’s take 3. 3 is a Prime Numbers because it can only be divided by itself and 1.
So, the prime divisors of number 3 are 3 and 1.
- 3 ÷ 1 = 3
- 1 ÷ 3 = 3
Greatest Common Divisor
Greatest Common Divisor refers to the greatest number that is a common divisor for the given set of numbers. In other words, GCD is a greatest positive number which is a common factor of both the positive integers.
Let’s find out the GCD of (13,46)
- Divisors of 13 = 1 and 13
- Divisors of 46 = 1,2,23 and 46
The common divisor of 13 and 46 is 1.
Thus, GCD of 13 and 46 is 1.
Therefore, GCD (13,46) = 1
Divisors in Maths
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.
Table of Content
- What are Divisors?
- Properties of Divisors
- Divisors and Dividends
- Divisor in Number Theory
- Examples of Divisors
- What are Prime Divisors?
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