# Factors of 371

Factors of 371 are 1, 7, 53, and 371

#### How to find factors of a number

 1.   Find factors of 371 using Division Method 2.   Find factors of 371 using Prime Factorization 3.   Find factors of 371 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 371

• Divide 371 by 1: 371 ÷ 1 : Remainder = 0
• Divide 371 by 7: 371 ÷ 7 : Remainder = 0
• Divide 371 by 53: 371 ÷ 53 : Remainder = 0
• Divide 371 by 371: 371 ÷ 371 : Remainder = 0

Hence, Factors of 371 are 1, 7, 53, and 371

#### 2. Steps to find factors of 371 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 371 using the division method, follow these steps:

• Step 1. Start dividing 371 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 371, which is 7. Divide 371 by 7 to obtain the quotient (53).
371 ÷ 7 = 53
• Step 3. Repeat step 1 with the obtained quotient (53).
53 ÷ 53 = 1

So, the prime factorization of 371 is, 371 = 7 x 53.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 371 as shown below:

So, the prime factorization of 371 is, 371 = 7 x 53.

#### 3. Find factors of 371 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 371 would be the two numbers which, when multiplied, give 371 as the result.

The following table represents the calculation of factors of 371 in pairs:

Factor Pair Pair Factorization
1 and 371 1 x 371 = 371
7 and 53 7 x 53 = 371

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 371. They are called negative pair factors.

Hence, the negative pairs of 371 would be ( -1 , -371 ) , ( -7 , -53 ) .

#### 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 number is a factor of zero (0), since 371 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, 7, 53, 371 are exact divisors of 371.
• Factors of 371 are 1, 7, 53, 371. Each factor divides 371 without leaving a remainder.

• What two numbers make 371?

Two numbers that make 371 are 7 and 53.

• What is prime factorization of 371?

Prime factorization of 371 is 7 x 53.

• Write some multiples of 371?

First five multiples of 371 are 742, 1113, 1484, 1855.

• Which is the smallest prime factor of 371?

The smallest prime factor of 371 is 7.

• Is 371 a perfect square?

No 371 is not a perfect square.

• What is the sum of all factors of 371?

The sum of all factors of 371 is 432.

• What are factors of 371?

Factors of 371 are 1, 7, 53, 371.

• How do you find factors of a negative number? ( eg. -371 )?

Factors of -371 are -1, -7, -53, -371.

• Is 371 a whole number?

Yes 371 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 371. Help him in finding the mean of 371.

Factors of 371 are 1, 7, 53, 371.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 371 is 1 + 7 + 53 + 371 = 432.
Hence, the mean of factors of 371 is 432 ÷ 4 = 108.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 371? Help her in writing all the factors.

Positive factors are 1, 7, 53, 371.
Negative factors are -1, -7, -53, -371.

Joey wants to write all the prime factors of 371 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 371 are 7, 53.
So in exponential form it can be written as 7 x 53.

Kevin has been asked to write 3 factor(s) of 371. Can you predict the answer?

3 factor(s) of 371 are 1, 7, 53.

Sammy is puzzled while calculating the prime factors of 371. Can you help him find them?

Factors of 371 are 1, 7, 53, 371.
Prime factors of 371 are 7, 53

What is prime factorization of 371?

Prime factorization of 371 is 7 x 53 = 7 x 53.

Can you help Rubel to find out the product of the even factors of 371?

Factors of 371 are 1, 7, 53, 371.
Even factors of 371 are 0.
Hence, product of even factors of 371 is; 0 = 0.