# Factors of 10101

Factors of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, and 10101

#### How to find factors of a number

 1.   Find factors of 10101 using Division Method 2.   Find factors of 10101 using Prime Factorization 3.   Find factors of 10101 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 10101

• Divide 10101 by 1: 10101 ÷ 1 : Remainder = 0
• Divide 10101 by 3: 10101 ÷ 3 : Remainder = 0
• Divide 10101 by 7: 10101 ÷ 7 : Remainder = 0
• Divide 10101 by 13: 10101 ÷ 13 : Remainder = 0
• Divide 10101 by 21: 10101 ÷ 21 : Remainder = 0
• Divide 10101 by 37: 10101 ÷ 37 : Remainder = 0
• Divide 10101 by 39: 10101 ÷ 39 : Remainder = 0
• Divide 10101 by 91: 10101 ÷ 91 : Remainder = 0
• Divide 10101 by 111: 10101 ÷ 111 : Remainder = 0
• Divide 10101 by 259: 10101 ÷ 259 : Remainder = 0
• Divide 10101 by 273: 10101 ÷ 273 : Remainder = 0
• Divide 10101 by 481: 10101 ÷ 481 : Remainder = 0
• Divide 10101 by 777: 10101 ÷ 777 : Remainder = 0
• Divide 10101 by 1443: 10101 ÷ 1443 : Remainder = 0
• Divide 10101 by 3367: 10101 ÷ 3367 : Remainder = 0
• Divide 10101 by 10101: 10101 ÷ 10101 : Remainder = 0

Hence, Factors of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, and 10101

#### 2. Steps to find factors of 10101 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 10101 using the division method, follow these steps:

• Step 1. Start dividing 10101 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 10101, which is 3. Divide 10101 by 3 to obtain the quotient (3367).
10101 ÷ 3 = 3367
• Step 3. Repeat step 1 with the obtained quotient (3367).
3367 ÷ 7 = 481
481 ÷ 13 = 37
37 ÷ 37 = 1

So, the prime factorization of 10101 is, 10101 = 3 x 7 x 13 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 10101 as shown below:

So, the prime factorization of 10101 is, 10101 = 3 x 7 x 13 x 37.

#### 3. Find factors of 10101 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 10101 would be the two numbers which, when multiplied, give 10101 as the result.

The following table represents the calculation of factors of 10101 in pairs:

Factor Pair Pair Factorization
1 and 10101 1 x 10101 = 10101
3 and 3367 3 x 3367 = 10101
7 and 1443 7 x 1443 = 10101
13 and 777 13 x 777 = 10101
21 and 481 21 x 481 = 10101
37 and 273 37 x 273 = 10101
39 and 259 39 x 259 = 10101
91 and 111 91 x 111 = 10101

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 10101. They are called negative pair factors.

Hence, the negative pairs of 10101 would be ( -1 , -10101 ) , ( -3 , -3367 ) , ( -7 , -1443 ) , ( -13 , -777 ) , ( -21 , -481 ) , ( -37 , -273 ) , ( -39 , -259 ) and ( -91 , -111 ) .

#### 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, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101 are exact divisors of 10101.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 10101 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 10101.

• What are the prime factors of 10101?

The factors of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.
Prime factors of 10101 are 3, 7, 13, 37.

• What two numbers make 10101?

Two numbers that make 10101 are 3 and 3367.

• What is the greatest prime factors of 10101?

The greatest prime factor of 10101 is 37.

• What are factors of 10101?

Factors of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.

• How do you find factors of a negative number? ( eg. -10101 )?

Factors of -10101 are -1, -3, -7, -13, -21, -37, -39, -91, -111, -259, -273, -481, -777, -1443, -3367, -10101.

• What are five multiples of 10101?

First five multiples of 10101 are 20202, 30303, 40404, 50505, 60606.

• Write some multiples of 10101?

First five multiples of 10101 are 20202, 30303, 40404, 50505.

• Is 10101 a perfect square?

No 10101 is not a perfect square.

• What two numbers make 10101?

Two numbers that make 10101 are 3 and 3367.

#### Examples of Factors

What is prime factorization of 10101?

Prime factorization of 10101 is 3 x 7 x 13 x 37 = 3 x 7 x 13 x 37.

Sammy is puzzled while calculating the prime factors of 10101. Can you help him find them?

Factors of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.
Prime factors of 10101 are 3, 7, 13, 37

Kevin has been asked to write 15 factor(s) of 10101. Can you predict the answer?

15 factor(s) of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367.

Joey wants to write all the prime factors of 10101 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 10101 are 3, 7, 13, 37.
So in exponential form it can be written as 3 x 7 x 13 x 37.

How many factors are there for 10101?

Factors of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.
So there are in total 16 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 10101? Help her in writing all the factors.

Positive factors are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.
Negative factors are -1, -3, -7, -13, -21, -37, -39, -91, -111, -259, -273, -481, -777, -1443, -3367, -10101.

Can you help Rubel to find out the product of the even factors of 10101?

Factors of 10101 are 1, 3, 7, 13, 21, 37, 39, 91, 111, 259, 273, 481, 777, 1443, 3367, 10101.
Even factors of 10101 are 0.
Hence, product of even factors of 10101 is; 0 = 0.