Factors of 1400

The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, and 1400

Positive Factors: These are positive divisors of 1400. Positive factors: 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400

Negative Factors: These are the negative counterparts of the positive factors.
Negative factors:  -1, -2, -4, -5, -7, -8, -10, -14, -20, -25, -28, -35, -50, -56, -70, -100, -140, -175, -200, -280, -350, -700, -1400.

Prime Factors: Prime factors are the prime numbers which, when multiplied together, give 1400 as the product.
Prime factors: 2, 5, 7.
 

Prime Factorization: Prime factorization involves breaking 1400 into its prime factors.
It is expressed as 2³×5²×7¹

Table Listing the Factors of 1400
 

This breakdown helps in understanding the various factors of 1400, 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 1400.

Methods to find the factors of 1400:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree

The multiplication method finds the pair of factors that give 1400 as their product.
 

Step 1: Find the pair of numbers whose product is 1400.
 

Step 2: The factors are those numbers, when multiplied, give 1400.
 

Step 3: Make a list of numbers whose product will be 1400.

A list of numbers whose products are 1400 is given below:

• 1 × 1400 = 1400
• 2 × 700 = 1400
• 4 × 350 = 1400
• 5 × 280 = 1400

Thus, the factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, and 1400.

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: 1400÷1=1400.
 

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 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, and 1400.

Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using its factors and expressed in terms of prime factors, represents its prime factorization.
Prime Factors of 1400: Number 1400 has three prime factors.
Prime factors: 2, 5, 7.
To find the prime factors of 1400:
 

Step 1: Divide 1400 with the smallest prime number (2).
1400÷2=700.
 

Step 2: Continue dividing the quotient (700) with 2 until no longer divisible.
700÷2=350

350÷2=175.
 

Step 3: Move to the next prime number (5) and repeat the division.
175÷5=35.
 

Step 4: Divide by 7.
7÷7=17

Thus, the prime factorization of 1400 is 2³×5²×7¹

The prime factorization is visually represented using the factor tree. It helps to understand the process easily.

This tree shows the breakdown of 1400 into its prime factors: 2³×5²×7¹.

In this factor tree, each branch splits into prime factors.

 

Positive and Negative Factor Pairs of 1400

Factors of 1400 can be written in both positive pairs and negative pairs. They are like team members. Their product will be equal to the number given.

Positive Factor Pairs: (1,1400), (2,700), (4,350), ..., (35,40).
 

Negative Factor Pairs: (-1,-1400), (-2,-700), (-4,-350), ..., (-35,-40).
 

• Factors: Numbers that divide a given number completely without leaving a remainder. For example, factors of 1400 include 1, 2, 5, 7, 10, and so on.
   
• Prime Factorization: The process of expressing a number as the product of its prime factors. For 1400, it is 2³×5²×7¹
   
• Factor Tree: A visual representation used to break down a number into its prime factors systematically.
   
• Positive Factors: Positive numbers that divide a given number completely without leaving a remainder. For 1400, they are 1, 2, 4, 5, ..., 1400.
   
• Perfect Square Factor: A factor that is a perfect square, meaning it is the result of a number multiplied by itself. For 1400, examples include 1, 4, 25, and 100.