# Factors of 1300

Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, and 1300

#### How to find factors of a number

 1.   Find factors of 1300 using Division Method 2.   Find factors of 1300 using Prime Factorization 3.   Find factors of 1300 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1300

• Divide 1300 by 1: 1300 ÷ 1 : Remainder = 0
• Divide 1300 by 2: 1300 ÷ 2 : Remainder = 0
• Divide 1300 by 4: 1300 ÷ 4 : Remainder = 0
• Divide 1300 by 5: 1300 ÷ 5 : Remainder = 0
• Divide 1300 by 10: 1300 ÷ 10 : Remainder = 0
• Divide 1300 by 13: 1300 ÷ 13 : Remainder = 0
• Divide 1300 by 20: 1300 ÷ 20 : Remainder = 0
• Divide 1300 by 25: 1300 ÷ 25 : Remainder = 0
• Divide 1300 by 26: 1300 ÷ 26 : Remainder = 0
• Divide 1300 by 50: 1300 ÷ 50 : Remainder = 0
• Divide 1300 by 52: 1300 ÷ 52 : Remainder = 0
• Divide 1300 by 65: 1300 ÷ 65 : Remainder = 0
• Divide 1300 by 100: 1300 ÷ 100 : Remainder = 0
• Divide 1300 by 130: 1300 ÷ 130 : Remainder = 0
• Divide 1300 by 260: 1300 ÷ 260 : Remainder = 0
• Divide 1300 by 325: 1300 ÷ 325 : Remainder = 0
• Divide 1300 by 650: 1300 ÷ 650 : Remainder = 0
• Divide 1300 by 1300: 1300 ÷ 1300 : Remainder = 0

Hence, Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, and 1300

#### 2. Steps to find factors of 1300 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 1300 using the division method, follow these steps:

• Step 1. Start dividing 1300 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 1300, which is 2. Divide 1300 by 2 to obtain the quotient (650).
1300 ÷ 2 = 650
• Step 3. Repeat step 1 with the obtained quotient (650).
650 ÷ 2 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1

So, the prime factorization of 1300 is, 1300 = 2 x 2 x 5 x 5 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1300 as shown below:

So, the prime factorization of 1300 is, 1300 = 2 x 2 x 5 x 5 x 13.

#### 3. Find factors of 1300 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 1300 would be the two numbers which, when multiplied, give 1300 as the result.

The following table represents the calculation of factors of 1300 in pairs:

Factor Pair Pair Factorization
1 and 1300 1 x 1300 = 1300
2 and 650 2 x 650 = 1300
4 and 325 4 x 325 = 1300
5 and 260 5 x 260 = 1300
10 and 130 10 x 130 = 1300
13 and 100 13 x 100 = 1300
20 and 65 20 x 65 = 1300
25 and 52 25 x 52 = 1300
26 and 50 26 x 50 = 1300

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 1300. They are called negative pair factors.

Hence, the negative pairs of 1300 would be ( -1 , -1300 ) , ( -2 , -650 ) , ( -4 , -325 ) , ( -5 , -260 ) , ( -10 , -130 ) , ( -13 , -100 ) , ( -20 , -65 ) , ( -25 , -52 ) and ( -26 , -50 ) .

#### 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. 1300 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1300.
• Every number is a factor of zero (0), since 1300 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, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300 are exact divisors of 1300.
• Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300. Each factor divides 1300 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300 are all less than or equal to 1300.

• Is 1300 a perfect square?

No 1300 is not a perfect square.

• What are factors of 1300?

Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300.

• Which is greatest factor of 1300?

The greatest factor of 1300 is 650.

• What is the sum of all factors of 1300?

The sum of all factors of 1300 is 3038.

• What are multiples of 1300?

First five multiples of 1300 are 2600, 3900, 5200, 6500.

• What is the greatest prime factors of 1300?

The greatest prime factor of 1300 is 13.

• What are six multiples of 1300?

First five multiples of 1300 are 2600, 3900, 5200, 6500, 7800, 9100.

• What is prime factorization of 1300?

Prime factorization of 1300 is 2 x 2 x 5 x 5 x 13.

• Is 1300 a whole number?

Yes 1300 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 1300? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300.
Negative factors are -1, -2, -4, -5, -10, -13, -20, -25, -26, -50, -52, -65, -100, -130, -260, -325, -650, -1300.

Can you help Sammy find out the product of the odd factors of 1300?

Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300.
Odd factors of 1300 are 1, 5, 13, 25, 65, 325.
Hence product of odd factors of 1300 is; 1 x 5 x 13 x 25 x 65 x 325 = 34328125.

Joey wants to write all the prime factors of 1300 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1300 are 2, 2, 5, 5, 13.
So in exponential form it can be written as 22 x 52 x 13.

How many factors are there for 1300?

Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300.
So there are in total 18 factors.

Kevin has been asked to write 17 factor(s) of 1300. Can you predict the answer?

17 factor(s) of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650.

Sammy is puzzled while calculating the prime factors of 1300. Can you help him find them?

Factors of 1300 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650, 1300.
Prime factors of 1300 are 2, 2, 5, 5, 13

What is prime factorization of 1300?

Prime factorization of 1300 is 2 x 2 x 5 x 5 x 13 = 22 x 52 x 13.