# Factors of 1400

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

#### How to find factors of a number

 1.   Find factors of 1400 using Division Method 2.   Find factors of 1400 using Prime Factorization 3.   Find factors of 1400 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1400

• Divide 1400 by 1: 1400 ÷ 1 : Remainder = 0
• Divide 1400 by 2: 1400 ÷ 2 : Remainder = 0
• Divide 1400 by 4: 1400 ÷ 4 : Remainder = 0
• Divide 1400 by 5: 1400 ÷ 5 : Remainder = 0
• Divide 1400 by 7: 1400 ÷ 7 : Remainder = 0
• Divide 1400 by 8: 1400 ÷ 8 : Remainder = 0
• Divide 1400 by 10: 1400 ÷ 10 : Remainder = 0
• Divide 1400 by 14: 1400 ÷ 14 : Remainder = 0
• Divide 1400 by 20: 1400 ÷ 20 : Remainder = 0
• Divide 1400 by 25: 1400 ÷ 25 : Remainder = 0
• Divide 1400 by 28: 1400 ÷ 28 : Remainder = 0
• Divide 1400 by 35: 1400 ÷ 35 : Remainder = 0
• Divide 1400 by 40: 1400 ÷ 40 : Remainder = 0
• Divide 1400 by 50: 1400 ÷ 50 : Remainder = 0
• Divide 1400 by 56: 1400 ÷ 56 : Remainder = 0
• Divide 1400 by 70: 1400 ÷ 70 : Remainder = 0
• Divide 1400 by 100: 1400 ÷ 100 : Remainder = 0
• Divide 1400 by 140: 1400 ÷ 140 : Remainder = 0
• Divide 1400 by 175: 1400 ÷ 175 : Remainder = 0
• Divide 1400 by 200: 1400 ÷ 200 : Remainder = 0
• Divide 1400 by 280: 1400 ÷ 280 : Remainder = 0
• Divide 1400 by 350: 1400 ÷ 350 : Remainder = 0
• Divide 1400 by 700: 1400 ÷ 700 : Remainder = 0
• Divide 1400 by 1400: 1400 ÷ 1400 : Remainder = 0

Hence, 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

#### 2. Steps to find factors of 1400 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 1400 using the division method, follow these steps:

• Step 1. Start dividing 1400 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 1400, which is 2. Divide 1400 by 2 to obtain the quotient (700).
1400 ÷ 2 = 700
• Step 3. Repeat step 1 with the obtained quotient (700).
700 ÷ 2 = 350
350 ÷ 2 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 1400 is, 1400 = 2 x 2 x 2 x 5 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1400 as shown below:

So, the prime factorization of 1400 is, 1400 = 2 x 2 x 2 x 5 x 5 x 7.

#### 3. Find factors of 1400 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 1400 would be the two numbers which, when multiplied, give 1400 as the result.

The following table represents the calculation of factors of 1400 in pairs:

Factor Pair Pair Factorization
1 and 1400 1 x 1400 = 1400
2 and 700 2 x 700 = 1400
4 and 350 4 x 350 = 1400
5 and 280 5 x 280 = 1400
7 and 200 7 x 200 = 1400
8 and 175 8 x 175 = 1400
10 and 140 10 x 140 = 1400
14 and 100 14 x 100 = 1400
20 and 70 20 x 70 = 1400
25 and 56 25 x 56 = 1400
28 and 50 28 x 50 = 1400
35 and 40 35 x 40 = 1400

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 1400. They are called negative pair factors.

Hence, the negative pairs of 1400 would be ( -1 , -1400 ) , ( -2 , -700 ) , ( -4 , -350 ) , ( -5 , -280 ) , ( -7 , -200 ) , ( -8 , -175 ) , ( -10 , -140 ) , ( -14 , -100 ) , ( -20 , -70 ) , ( -25 , -56 ) , ( -28 , -50 ) and ( -35 , -40 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 1400 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1400.
• Every number is a factor of zero (0), since 1400 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 are exact divisors of 1400.
• 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, 1400. Each factor divides 1400 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 are all less than or equal to 1400.

• What are the pair factors of 1400?

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

• What are five multiples of 1400?

First five multiples of 1400 are 2800, 4200, 5600, 7000, 8400.

• What two numbers make 1400?

Two numbers that make 1400 are 2 and 700.

• What is the sum of all factors of 1400?

The sum of all factors of 1400 is 3720.

• What are factors of -1400?

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, -1400.

• What are factors of 1400?

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, 1400.

• Is 1400 a perfect square?

No 1400 is not a perfect square.

• Which is the smallest prime factor of 1400?

Smallest prime factor of 1400 is 2.

• Which is greatest factor of 1400?

The greatest factor of 1400 is 700.

#### Examples of Factors

Can you help Sammy find out the product of the odd factors of 1400?

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, 1400.
Odd factors of 1400 are 1, 5, 7, 25, 35, 175.
Hence product of odd factors of 1400 is; 1 x 5 x 7 x 25 x 35 x 175 = 5359375.

Joey wants to write all the prime factors of 1400 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1400 are 2, 2, 2, 5, 5, 7.
So in exponential form it can be written as 23 x 52 x 7.

How many factors are there for 1400?

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, 1400.
So there are in total 24 factors.

Kevin has been asked to write 23 factor(s) of 1400. Can you predict the answer?

23 factor(s) 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.

Sammy is puzzled while calculating the prime factors of 1400. Can you help him find them?

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, 1400.
Prime factors of 1400 are 2, 2, 2, 5, 5, 7

What is prime factorization of 1400?

Prime factorization of 1400 is 2 x 2 x 2 x 5 x 5 x 7 = 23 x 52 x 7.

Can you help Rubel to find out the product of the even factors of 1400?

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, 1400.
Even factors of 1400 are 2, 4, 8, 10, 14, 20, 28, 40, 50, 56, 70, 100, 140, 200, 280, 350, 700, 1400.
Hence, product of even factors of 1400 is; 2 x 4 x 8 x 10 x 14 x 20 x 28 x 40 x 50 x 56 x 70 x 100 x 140 x 200 x 280 x 350 x 700 x 1400 = 1.0578455953408e+31.