# Factors of 409

Factors of 409 are 1 and 409

#### How to find factors of a number

 1.   Find factors of 409 using Division Method 2.   Find factors of 409 using Prime Factorization 3.   Find factors of 409 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 409

• Divide 409 by 1: 409 ÷ 1 : Remainder = 0
• Divide 409 by 409: 409 ÷ 409 : Remainder = 0

Hence, Factors of 409 are 1 and 409

#### 2. Steps to find factors of 409 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 409 using the division method, follow these steps:

• Step 1. Start dividing 409 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 409, which is 409. Divide 409 by 409 to obtain the quotient (1).
409 ÷ 409 = 1
• Step 3. Repeat step 1 with the obtained quotient (1).

So, the prime factorization of 409 is, 409 = 409.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 409 as shown below:

So, the prime factorization of 409 is, 409 = 409.

#### 3. Find factors of 409 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 409 would be the two numbers which, when multiplied, give 409 as the result.

The following table represents the calculation of factors of 409 in pairs:

Factor Pair Pair Factorization
1 and 409 1 x 409 = 409

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 409. They are called negative pair factors.

Hence, the negative pairs of 409 would be ( -1 , -409 ) , .

#### How can we define factors?

In mathematics, a factor is a number which divides into another number exactly, without leaving any remainder. A factor of a number can be positive of negative.

#### Properties of factors

• Every factor of a number is an exact divisor of that number, example 1, 409 are exact divisors of 409.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Each number is a factor of itself. Eg. 409 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 409.

• Is 409 a perfect square?

No 409 is not a perfect square.

• What are factors of 409?

Factors of 409 are 1, 409.

• Which is greatest factor of 409?

The greatest factor of 409 is 1.

• What is the sum of all factors of 409?

The sum of all factors of 409 is 410.

• What are multiples of 409?

First five multiples of 409 are 818, 1227, 1636, 2045.

• What is the greatest prime factors of 409?

The greatest prime factor of 409 is 409.

• What are six multiples of 409?

First five multiples of 409 are 818, 1227, 1636, 2045, 2454, 2863.

• What is prime factorization of 409?

Prime factorization of 409 is 409.

• Is 409 a whole number?

Yes 409 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 409? Help her in writing all the factors.

Positive factors are 1, 409.
Negative factors are -1, -409.

Can you help Sammy find out the product of the odd factors of 409?

Factors of 409 are 1, 409.
Odd factors of 409 are 1, 409.
Hence product of odd factors of 409 is; 1 x 409 = 409.

Joey wants to write all the prime factors of 409 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 409 are 409.
So in exponential form it can be written as 409.

How many factors are there for 409?

Factors of 409 are 1, 409.
So there are in total 2 factors.

Kevin has been asked to write 1 factor(s) of 409. Can you predict the answer?

1 factor(s) of 409 is 1.

Sammy is puzzled while calculating the prime factors of 409. Can you help him find them?

Factors of 409 are 1, 409.
Prime factors of 409 are 409

What is prime factorization of 409?

Prime factorization of 409 is 409 = 409.