1. Steps to find factors of 406 using Division Method

Example: Find factors of 406

  • Divide 406 by 1: 406 ÷ 1 : Remainder = 0
  • Divide 406 by 2: 406 ÷ 2 : Remainder = 0
  • Divide 406 by 7: 406 ÷ 7 : Remainder = 0
  • Divide 406 by 14: 406 ÷ 14 : Remainder = 0
  • Divide 406 by 29: 406 ÷ 29 : Remainder = 0
  • Divide 406 by 58: 406 ÷ 58 : Remainder = 0
  • Divide 406 by 203: 406 ÷ 203 : Remainder = 0
  • Divide 406 by 406: 406 ÷ 406 : Remainder = 0

Hence, Factors of 406 are 1, 2, 7, 14, 29, 58, 203, and 406

2. Steps to find factors of 406 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 406 using the division method, follow these steps:

  • Step 1. Start dividing 406 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 406, which is 2. Divide 406 by 2 to obtain the quotient (203).
    406 ÷ 2 = 203
  • Step 3. Repeat step 1 with the obtained quotient (203).
    203 ÷ 7 = 29
    29 ÷ 29 = 1

So, the prime factorization of 406 is, 406 = 2 x 7 x 29.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 406 as shown below:

So, the prime factorization of 406 is, 406 = 2 x 7 x 29.

3. Find factors of 406 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 406 would be the two numbers which, when multiplied, give 406 as the result.

The following table represents the calculation of factors of 406 in pairs:

Factor Pair Pair Factorization
1 and 406 1 x 406 = 406
2 and 203 2 x 203 = 406
7 and 58 7 x 58 = 406
14 and 29 14 x 29 = 406

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 406. They are called negative pair factors.

Hence, the negative pairs of 406 would be ( -1 , -406 ) , ( -2 , -203 ) , ( -7 , -58 ) and ( -14 , -29 ) .

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

  • Each number is a factor of itself. Eg. 406 is a factor of itself.
  • 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, 2, 7, 14, 29, 58, 203, 406 are exact divisors of 406.
  • 1 is a factor of every number. Eg. 1 is a factor of 406.
  • Every number is a factor of zero (0), since 406 x 0 = 0.

Frequently Asked Questions

  • What are the prime factors of 406?

    The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406.
    Prime factors of 406 are 2, 7, 29.

  • What is the sum of all factors of 406?

    The sum of all factors of 406 is 720.

  • What are the pair factors of 406?

    Pair factors of 406 are (1,406), (2,203), (7,58), (14,29).

  • What two numbers make 406?

    Two numbers that make 406 are 2 and 203.

  • What are multiples of 406?

    First five multiples of 406 are 812, 1218, 1624, 2030.

  • Is 406 a perfect square?

    No 406 is not a perfect square.

  • Which is greatest factor of 406?

    The greatest factor of 406 is 203.

  • How do you factors of 406?

    Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406.

  • What are five multiples of 406?

    First five multiples of 406 are 812, 1218, 1624, 2030, 2436.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 406?

Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406.
Even factors of 406 are 2, 14, 58, 406.
Hence, product of even factors of 406 is; 2 x 14 x 58 x 406 = 659344.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 406? Help her in writing all the factors.

Positive factors are 1, 2, 7, 14, 29, 58, 203, 406.
Negative factors are -1, -2, -7, -14, -29, -58, -203, -406.

How many factors are there for 406?

Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406.
So there are in total 8 factors.

Sammy is puzzled while calculating the prime factors of 406. Can you help him find them?

Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406.
Prime factors of 406 are 2, 7, 29

Joey wants to write all the prime factors of 406 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 406 are 2, 7, 29.
So in exponential form it can be written as 2 x 7 x 29.

What is prime factorization of 406?

Prime factorization of 406 is 2 x 7 x 29 = 2 x 7 x 29.

Can you help Rubel to find out the product of the even factors of 406?

Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406.
Even factors of 406 are 2, 14, 58, 406.
Hence, product of even factors of 406 is; 2 x 14 x 58 x 406 = 659344.