# Factors of 301

Factors of 301 are 1, 7, 43, and 301

#### How to find factors of a number

 1.   Find factors of 301 using Division Method 2.   Find factors of 301 using Prime Factorization 3.   Find factors of 301 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 301

• Divide 301 by 1: 301 ÷ 1 : Remainder = 0
• Divide 301 by 7: 301 ÷ 7 : Remainder = 0
• Divide 301 by 43: 301 ÷ 43 : Remainder = 0
• Divide 301 by 301: 301 ÷ 301 : Remainder = 0

Hence, Factors of 301 are 1, 7, 43, and 301

#### 2. Steps to find factors of 301 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 301 using the division method, follow these steps:

• Step 1. Start dividing 301 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 301, which is 7. Divide 301 by 7 to obtain the quotient (43).
301 ÷ 7 = 43
• Step 3. Repeat step 1 with the obtained quotient (43).
43 ÷ 43 = 1

So, the prime factorization of 301 is, 301 = 7 x 43.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 301 as shown below:

So, the prime factorization of 301 is, 301 = 7 x 43.

#### 3. Find factors of 301 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 301 would be the two numbers which, when multiplied, give 301 as the result.

The following table represents the calculation of factors of 301 in pairs:

Factor Pair Pair Factorization
1 and 301 1 x 301 = 301
7 and 43 7 x 43 = 301

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 301. They are called negative pair factors.

Hence, the negative pairs of 301 would be ( -1 , -301 ) , ( -7 , -43 ) .

#### 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, 43, 301 are exact divisors of 301.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 301 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 301.

• Is 301 a perfect square?

No 301 is not a perfect square.

• What are factors of 301?

Factors of 301 are 1, 7, 43, 301.

• Which is greatest factor of 301?

The greatest factor of 301 is 43.

• What is the sum of all factors of 301?

The sum of all factors of 301 is 352.

• What are multiples of 301?

First five multiples of 301 are 602, 903, 1204, 1505.

• What is the greatest prime factors of 301?

The greatest prime factor of 301 is 43.

• What are six multiples of 301?

First five multiples of 301 are 602, 903, 1204, 1505, 1806, 2107.

• What is prime factorization of 301?

Prime factorization of 301 is 7 x 43.

• Is 301 a whole number?

Yes 301 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 301? Help her in writing all the factors.

Positive factors are 1, 7, 43, 301.
Negative factors are -1, -7, -43, -301.

Can you help Sammy find out the product of the odd factors of 301?

Factors of 301 are 1, 7, 43, 301.
Odd factors of 301 are 1, 7, 43, 301.
Hence product of odd factors of 301 is; 1 x 7 x 43 x 301 = 90601.

Joey wants to write all the prime factors of 301 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 301 are 7, 43.
So in exponential form it can be written as 7 x 43.

How many factors are there for 301?

Factors of 301 are 1, 7, 43, 301.
So there are in total 4 factors.

Kevin has been asked to write 3 factor(s) of 301. Can you predict the answer?

3 factor(s) of 301 are 1, 7, 43.

Sammy is puzzled while calculating the prime factors of 301. Can you help him find them?

Factors of 301 are 1, 7, 43, 301.
Prime factors of 301 are 7, 43

What is prime factorization of 301?

Prime factorization of 301 is 7 x 43 = 7 x 43.