# Factors of 10001

Factors of 10001 are 1, 73, 137, and 10001

#### How to find factors of a number

 1.   Find factors of 10001 using Division Method 2.   Find factors of 10001 using Prime Factorization 3.   Find factors of 10001 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 10001

• Divide 10001 by 1: 10001 ÷ 1 : Remainder = 0
• Divide 10001 by 73: 10001 ÷ 73 : Remainder = 0
• Divide 10001 by 137: 10001 ÷ 137 : Remainder = 0
• Divide 10001 by 10001: 10001 ÷ 10001 : Remainder = 0

Hence, Factors of 10001 are 1, 73, 137, and 10001

#### 2. Steps to find factors of 10001 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 10001 using the division method, follow these steps:

• Step 1. Start dividing 10001 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 10001, which is 73. Divide 10001 by 73 to obtain the quotient (137).
10001 ÷ 73 = 137
• Step 3. Repeat step 1 with the obtained quotient (137).
137 ÷ 137 = 1

So, the prime factorization of 10001 is, 10001 = 73 x 137.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 10001 as shown below:

So, the prime factorization of 10001 is, 10001 = 73 x 137.

#### 3. Find factors of 10001 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 10001 would be the two numbers which, when multiplied, give 10001 as the result.

The following table represents the calculation of factors of 10001 in pairs:

Factor Pair Pair Factorization
1 and 10001 1 x 10001 = 10001
73 and 137 73 x 137 = 10001

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 10001. They are called negative pair factors.

Hence, the negative pairs of 10001 would be ( -1 , -10001 ) , ( -73 , -137 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 73, 137, 10001 are exact divisors of 10001.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 10001 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 10001.

• What two numbers make 10001?

Two numbers that make 10001 are 73 and 137.

• What is prime factorization of 10001?

Prime factorization of 10001 is 73 x 137.

• Write some multiples of 10001?

First five multiples of 10001 are 20002, 30003, 40004, 50005.

• Which is the smallest prime factor of 10001?

The smallest prime factor of 10001 is 73.

• Is 10001 a perfect square?

No 10001 is not a perfect square.

• What is the sum of all factors of 10001?

The sum of all factors of 10001 is 10212.

• What are factors of 10001?

Factors of 10001 are 1, 73, 137, 10001.

• How do you find factors of a negative number? ( eg. -10001 )?

Factors of -10001 are -1, -73, -137, -10001.

• Is 10001 a whole number?

Yes 10001 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 10001. Help him in finding the mean of 10001.

Factors of 10001 are 1, 73, 137, 10001.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 10001 is 1 + 73 + 137 + 10001 = 10212.
Hence, the mean of factors of 10001 is 10212 ÷ 4 = 2553.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 10001? Help her in writing all the factors.

Positive factors are 1, 73, 137, 10001.
Negative factors are -1, -73, -137, -10001.

Joey wants to write all the prime factors of 10001 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 10001 are 73, 137.
So in exponential form it can be written as 73 x 137.

Kevin has been asked to write 3 factor(s) of 10001. Can you predict the answer?

3 factor(s) of 10001 are 1, 73, 137.

Sammy is puzzled while calculating the prime factors of 10001. Can you help him find them?

Factors of 10001 are 1, 73, 137, 10001.
Prime factors of 10001 are 73, 137

What is prime factorization of 10001?

Prime factorization of 10001 is 73 x 137 = 73 x 137.

Can you help Rubel to find out the product of the even factors of 10001?

Factors of 10001 are 1, 73, 137, 10001.
Even factors of 10001 are 0.
Hence, product of even factors of 10001 is; 0 = 0.