Factors of 249

While multiplying two positive numbers, those two numbers become the factors of their  product. Factors have the following properties:

• The smallest factor of any number is 1.
• A number has a finite number of factors.
• Factors are always less than or equal to the number, except the prime numbers which have only 1 and the number itself. 
• Division and multiplication operations are used for finding factors.

The factors of 249 are 1, 3, 83, and 249.

Negative Factors of 249: -1, -3, -83, and -249
Prime Factors of 249: 3 and 83
Prime Factorization of 249: 3 x 83
The Sum of Factors of 249: 336
 

We can find the factors using multiplication and division. Let us look at these methods in detail.

• Multiplication
• Division Method
   

While multiplying two whole numbers, we get a product, then the two whole numbers are called factors.
For example, to find the factors of 12, we can use the following steps

1  12 = 12
2  6 = 12              
3  4 = 12
4  3 = 12

As a result, the factors of 12 are 1, 2, 3, 4, and 12.  
 

The division method helps us find all factors of a number. We need to check the numbers upto the square root of the given number. Lets find the factors of 10 using following steps.

Step 1: Start with 1, 10/1 = 10, so 1 and 10 are factors.

Step 2: try with 2 next, 10/2 = 5, there is no remainder. So 2 and 5 are factors.

Step 3: Divide 10 by 3, we get the remainder as 1. So 3 is not a factor of 10.

Step 4: Continue dividing 10 by the numbers up to 3 (square root of 10 = 3.16).

As a result, the numbers 1, 2, 5, and 10 evenly divide 10 without leaving any remainder. Using this method, we have successfully found the factors of 10 to be 1, 2, 5, and 10.
 

Prime Factors: The factors which are prime numbers are called prime factors. For example, the factors of 6 are 1, 2, 3, and 6. Among these, 2 and 3 are the prime factors.

Prime Factorization: Reducing the number into its prime factors is called prime factorization. For example, the prime factors of 6 are 2 and 3. The prime factorization of 6 is 2  3.

Prime Factors of 249 - The prime factors of 249 are 3 and 83. Let us now verify the answer by using the methods mentioned below:

• Prime factorization
• Factor tree

Prime Factorization of 249 - Let us find out the prime factorization of 249.

Step 1: Start dividing the number by the small prime numbers. 249 is not divisible by 2 because the unit’s place digit is 9, which is an odd number.

Step 2: Next, divide 249 by 3 we get the quotient as 83, which is a prime number.

Step 3: The number 249 can be reduced to 3  83. 

The prime factorization of 249 is 3 x 83. 
 

The pictorial representation of prime factors of a number is called factor tree. Every branch in the tree is divided into factors. As soon as one of the factors at the end of the branch is a prime number, stop expanding the tree.

Factor tree of 249: 

The diagram above reveals that 1, 3, 83, and 249 are the factors of 249.

The prime factorization of 249 is 3 x  83. 
 

The set of two numbers whose product equals the original number is known as factor pairs. There are two types of factor pairs: Positive factor pairs and negative factor pairs.

Positive Pair Factors: (1, 249) and (3, 83)

 
Negative Pair Factors: (-1, -249) and (-3, -83)
 

• Greatest Common Factor (GCF): The largest number that divides two or more numbers evenly without leaving any remainder is called GCF.Example: The GCF of 249 and 3 is 3. This is because, among the factors of 249 and 3, 3 is greatest.

• Least Common Multiple (LCM): It is the smallest positive number that is a multiple of two or more numbers.Example: The LCM of 24 and 36 is 72.

• Prime Numbers: The numbers which can be disable by 1 and themselves are called prime numbers.Example: 2, 3, 5, 7, and 11 are prime numbers because they have only two factors.