# Factors of 2401

Factors of 2401 are 1, 7, 49, 343, and 2401

#### How to find factors of a number

 1.   Find factors of 2401 using Division Method 2.   Find factors of 2401 using Prime Factorization 3.   Find factors of 2401 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 2401

• Divide 2401 by 1: 2401 ÷ 1 : Remainder = 0
• Divide 2401 by 7: 2401 ÷ 7 : Remainder = 0
• Divide 2401 by 49: 2401 ÷ 49 : Remainder = 0
• Divide 2401 by 343: 2401 ÷ 343 : Remainder = 0
• Divide 2401 by 2401: 2401 ÷ 2401 : Remainder = 0

Hence, Factors of 2401 are 1, 7, 49, 343, and 2401

#### 2. Steps to find factors of 2401 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 2401 using the division method, follow these steps:

• Step 1. Start dividing 2401 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 2401, which is 7. Divide 2401 by 7 to obtain the quotient (343).
2401 ÷ 7 = 343
• Step 3. Repeat step 1 with the obtained quotient (343).
343 ÷ 7 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1

So, the prime factorization of 2401 is, 2401 = 7 x 7 x 7 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2401 as shown below:

So, the prime factorization of 2401 is, 2401 = 7 x 7 x 7 x 7.

#### 3. Find factors of 2401 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 2401 would be the two numbers which, when multiplied, give 2401 as the result.

The following table represents the calculation of factors of 2401 in pairs:

Factor Pair Pair Factorization
1 and 2401 1 x 2401 = 2401
7 and 343 7 x 343 = 2401
49 and 49 49 x 49 = 2401

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 2401. They are called negative pair factors.

Hence, the negative pairs of 2401 would be ( -1 , -2401 ) , ( -7 , -343 ) and ( -49 , -49 ) .

#### 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, 7, 49, 343, 2401 are exact divisors of 2401.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 2401 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 2401.

• Which is the smallest prime factor of 2401?

The smallest prime factor of 2401 is 7.

• Is 2401 a whole number?

Yes 2401 is a whole number.

• What are the prime factors of 2401?

The factors of 2401 are 1, 7, 49, 343, 2401.
Prime factors of 2401 are 7, 7, 7, 7.

• What two numbers make 2401?

Two numbers that make 2401 are 7 and 343.

• What are multiples of 2401?

First five multiples of 2401 are 4802, 7203, 9604, 12005.

• What is the sum of all factors of 2401?

The sum of all factors of 2401 is 2801.

• What are five multiples of 2401?

First five multiples of 2401 are 4802, 7203, 9604, 12005, 14406.

• Is 2401 a perfect square?

Yes 2401 is a perfect square.

• What is the greatest prime factors of 2401?

The greatest prime factor of 2401 is 7.

#### Examples of Factors

How many factors are there for 2401?

Factors of 2401 are 1, 7, 49, 343, 2401.
So there are in total 5 factors.

Kevin has been asked to write 4 factor(s) of 2401. Can you predict the answer?

4 factor(s) of 2401 are 1, 7, 49, 343.

Sammy is puzzled while calculating the prime factors of 2401. Can you help him find them?

Factors of 2401 are 1, 7, 49, 343, 2401.
Prime factors of 2401 are 7, 7, 7, 7

What is prime factorization of 2401?

Prime factorization of 2401 is 7 x 7 x 7 x 7 = 74.

Ariel has been assigned the task to find the product of all the prime factors of 2401. Can you help her?

Prime factors of 2401 are 7, 7, 7, 7.
Hence, the product of prime factors of 7.

Can you help Rubel to find out the product of the even factors of 2401?

Factors of 2401 are 1, 7, 49, 343, 2401.
Even factors of 2401 are 0.
Hence, product of even factors of 2401 is; 0 = 0.

Joy wants to calculate mean of all the factors of 2401. Help him in finding the mean of 2401.

Factors of 2401 are 1, 7, 49, 343, 2401.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 2401 is 1 + 7 + 49 + 343 + 2401 = 2801.
Hence, the mean of factors of 2401 is 2801 ÷ 5 = 560.20.