# Factors of 413

Factors of 413 are 1, 7, 59, and 413

#### How to find factors of a number

 1.   Find factors of 413 using Division Method 2.   Find factors of 413 using Prime Factorization 3.   Find factors of 413 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 413

• Divide 413 by 1: 413 ÷ 1 : Remainder = 0
• Divide 413 by 7: 413 ÷ 7 : Remainder = 0
• Divide 413 by 59: 413 ÷ 59 : Remainder = 0
• Divide 413 by 413: 413 ÷ 413 : Remainder = 0

Hence, Factors of 413 are 1, 7, 59, and 413

#### 2. Steps to find factors of 413 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 413 using the division method, follow these steps:

• Step 1. Start dividing 413 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 413, which is 7. Divide 413 by 7 to obtain the quotient (59).
413 ÷ 7 = 59
• Step 3. Repeat step 1 with the obtained quotient (59).
59 ÷ 59 = 1

So, the prime factorization of 413 is, 413 = 7 x 59.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 413 as shown below:

So, the prime factorization of 413 is, 413 = 7 x 59.

#### 3. Find factors of 413 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 413 would be the two numbers which, when multiplied, give 413 as the result.

The following table represents the calculation of factors of 413 in pairs:

Factor Pair Pair Factorization
1 and 413 1 x 413 = 413
7 and 59 7 x 59 = 413

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 413. They are called negative pair factors.

Hence, the negative pairs of 413 would be ( -1 , -413 ) , ( -7 , -59 ) .

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 7, 59, 413 are exact divisors of 413.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 413 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 413.

• What is prime factorization of 413?

Prime factorization of 413 is 7 x 59.

• How do you find factors of a negative number? ( eg. -413 )?

Factors of -413 are -1, -7, -59, -413.

• What are the prime factors of 413?

The factors of 413 are 1, 7, 59, 413.
Prime factors of 413 are 7, 59.

• What are pair factors of 413?

The pair factors of 413 are (1,413), (7,59).

• What is the greatest prime factors of 413?

The greatest prime factor of 413 is 59.

• What are six multiples of 413?

First five multiples of 413 are 826, 1239, 1652, 2065, 2478, 2891.

• What are factors of 413?

Factors of 413 are 1, 7, 59, 413.

• Which is the smallest prime factor of 413?

Smallest prime factor of 413 is 7.

• Is 413 a whole number?

Yes 413 is a whole number.

#### Examples of Factors

Kevin has been asked to write 3 factor(s) of 413. Can you predict the answer?

3 factor(s) of 413 are 1, 7, 59.

Sammy is puzzled while calculating the prime factors of 413. Can you help him find them?

Factors of 413 are 1, 7, 59, 413.
Prime factors of 413 are 7, 59

What is prime factorization of 413?

Prime factorization of 413 is 7 x 59 = 7 x 59.

Ariel has been assigned the task to find the product of all the prime factors of 413. Can you help her?

Prime factors of 413 are 7, 59.
Hence, the product of prime factors of 413.

Can you help Rubel to find out the product of the even factors of 413?

Factors of 413 are 1, 7, 59, 413.
Even factors of 413 are 0.
Hence, product of even factors of 413 is; 0 = 0.

Joy wants to calculate mean of all the factors of 413. Help him in finding the mean of 413.

Factors of 413 are 1, 7, 59, 413.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 413 is 1 + 7 + 59 + 413 = 480.
Hence, the mean of factors of 413 is 480 ÷ 4 = 120.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 413? Help her in writing all the factors.

Positive factors are 1, 7, 59, 413.
Negative factors are -1, -7, -59, -413.