# Factors of 407

Factors of 407 are 1, 11, 37, and 407

#### How to find factors of a number

 1.   Find factors of 407 using Division Method 2.   Find factors of 407 using Prime Factorization 3.   Find factors of 407 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 407

• Divide 407 by 1: 407 ÷ 1 : Remainder = 0
• Divide 407 by 11: 407 ÷ 11 : Remainder = 0
• Divide 407 by 37: 407 ÷ 37 : Remainder = 0
• Divide 407 by 407: 407 ÷ 407 : Remainder = 0

Hence, Factors of 407 are 1, 11, 37, and 407

#### 2. Steps to find factors of 407 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 407 using the division method, follow these steps:

• Step 1. Start dividing 407 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 407, which is 11. Divide 407 by 11 to obtain the quotient (37).
407 ÷ 11 = 37
• Step 3. Repeat step 1 with the obtained quotient (37).
37 ÷ 37 = 1

So, the prime factorization of 407 is, 407 = 11 x 37.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 407 as shown below:

So, the prime factorization of 407 is, 407 = 11 x 37.

#### 3. Find factors of 407 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 407 would be the two numbers which, when multiplied, give 407 as the result.

The following table represents the calculation of factors of 407 in pairs:

Factor Pair Pair Factorization
1 and 407 1 x 407 = 407
11 and 37 11 x 37 = 407

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 407. They are called negative pair factors.

Hence, the negative pairs of 407 would be ( -1 , -407 ) , ( -11 , -37 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 407 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, 11, 37, 407 are exact divisors of 407.
• Factors of 407 are 1, 11, 37, 407. Each factor divides 407 without leaving a remainder.

• What two numbers make 407?

Two numbers that make 407 are 11 and 37.

• What is prime factorization of 407?

Prime factorization of 407 is 11 x 37.

• Write some multiples of 407?

First five multiples of 407 are 814, 1221, 1628, 2035.

• Which is the smallest prime factor of 407?

The smallest prime factor of 407 is 11.

• Is 407 a perfect square?

No 407 is not a perfect square.

• What is the sum of all factors of 407?

The sum of all factors of 407 is 456.

• What are factors of 407?

Factors of 407 are 1, 11, 37, 407.

• How do you find factors of a negative number? ( eg. -407 )?

Factors of -407 are -1, -11, -37, -407.

• Is 407 a whole number?

Yes 407 is a whole number.

#### Examples of Factors

Joy wants to calculate mean of all the factors of 407. Help him in finding the mean of 407.

Factors of 407 are 1, 11, 37, 407.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 407 is 1 + 11 + 37 + 407 = 456.
Hence, the mean of factors of 407 is 456 ÷ 4 = 114.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 407? Help her in writing all the factors.

Positive factors are 1, 11, 37, 407.
Negative factors are -1, -11, -37, -407.

Joey wants to write all the prime factors of 407 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 407 are 11, 37.
So in exponential form it can be written as 11 x 37.

Kevin has been asked to write 3 factor(s) of 407. Can you predict the answer?

3 factor(s) of 407 are 1, 11, 37.

Sammy is puzzled while calculating the prime factors of 407. Can you help him find them?

Factors of 407 are 1, 11, 37, 407.
Prime factors of 407 are 11, 37

What is prime factorization of 407?

Prime factorization of 407 is 11 x 37 = 11 x 37.

Can you help Rubel to find out the product of the even factors of 407?

Factors of 407 are 1, 11, 37, 407.
Even factors of 407 are 0.
Hence, product of even factors of 407 is; 0 = 0.