Factors of 2240

The factors of 2240 are the numbers that divide 2240 evenly.

The factors of 2240 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240.
 

Positive factors: These are negative counterparts of the positive factors.
Positive factors: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 40, 44, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240
 

Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -32, -40, -44, -56, -64, -70, -80, -112, -140, -160, -224, -280, -320, -448, -560, -1120, -2240

Prime Factors and Prime Factorization
Prime factors are the prime numbers themselves, when multiplied together, give 2240 as the product. The prime factorization involves breaking 2240 into its prime factors. Prime factors of 2240: 2, 5, 7
 

Prime Factorization: Prime factorization involves expressing 2240 as the product of its prime factors.
Expressed as 2⁶×5¹×7¹
 

Table of Factors of 2240

This breakdown helps in understanding the various factors of 2240, whether they are positive or negative, as well as how prime factorization works for this number.
 

There are different methods to find the factors of 2240:
 

Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree

The multiplication method finds the pair of factors that give 2240 as their product.

Step 1: Find the pair of numbers whose product is 2240.

Step 2: The factors are those numbers, when multiplied, give 2240.

Step 3: Make a list of numbers whose product will be 2240.

A list of numbers whose products are 2240 is given below:

• 1 × 2240 = 2240
• 2 × 1120 = 2240
• 4 × 560 = 2240
• 5 × 448 = 2240
• 8 × 280 = 2240
• 10 × 224 = 2240
• 11 × 204 = 2240
• 16 × 140 = 2240
• 20 × 112 = 2240
• 22 × 102 = 2240
• 32 × 70 = 2240
• 40 × 56 = 2240
• 44 × 51 = 2240

Thus, the factors of 2240 are: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240.
 

The division method finds the numbers that fully divide the given number. The steps are given below:

Step 1: Since every number is divisible by 1, 1 will always be a factor.
Example: 2240 ÷ 1 = 2240
 

Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
 

Thus, the factors of 2240 are: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240.

Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using the factors of that number, is expressed in the form of prime factors, which is known as prime factorization.

Prime Factors of 2240: Number 2240 has prime factors of 2, 5, and 7.

To find the prime factors of 2240:

Divide 2240 by 2 repeatedly until you get an odd number:
2240 ÷ 2 = 1120
1120 ÷ 2 = 560
560 ÷ 2 = 280
280 ÷ 2 = 140
140 ÷ 2 = 70
70 ÷ 2 = 35

Now, divide 35 by 5:
35 ÷ 5 = 7

Finally, divide 7 by 7:
7 ÷ 7 = 1
 

Prime Factorization of 2240: 2⁶×5¹×7¹
 

The prime factorization can be visually represented using a factor tree, which helps to understand the breakdown process easily.

Positive and Negative Factor Pairs of 2240
Factors of 2240 can be written in both positive pairs and negative pairs. They are like team members whose product will be equal to the given number.
 

Positive Factor Pairs: (1, 2240), (2, 1120), (4, 560), (5, 448), (8, 280), (10, 224), (11, 204), (16, 140), (20, 112), (22, 102), (32, 70), (40, 56), (44, 51)
 

Negative Factor Pairs: (-1, -2240), (-2, -1120), (-4, -560), (-5, -448), (-8, -280), (-10, -224), (-11, -204), (-16, -140), (-20, -112), (-22, -102), (-32, -70), (-40, -56), (-44, -51)

• Factors: Numbers that can divide a given number completely without leaving a remainder. Example: 1, 2, 4, 5, etc., are factors of 2240.
   
• Prime Factors: Prime numbers that, when multiplied together, result in the original number. Example: 2, 5, and 7 are the prime factors of 2240.
   
• Prime Factorization: The process of breaking down a number into its prime factors. Example: The prime factorization of 2240 is 2⁶ × 5¹ × 7¹.
   
• Multiple: A number that is the product of a given number and an integer. Example: 112 is a multiple of 16 (since 16×7=112).
   
• Perfect Square: A number that is the product of an integer multiplied by itself. Example: 64 is a perfect square because 8×8=64.