1. Steps to find factors of 404 using Division Method

Example: Find factors of 404

  • Divide 404 by 1: 404 ÷ 1 : Remainder = 0
  • Divide 404 by 2: 404 ÷ 2 : Remainder = 0
  • Divide 404 by 4: 404 ÷ 4 : Remainder = 0
  • Divide 404 by 101: 404 ÷ 101 : Remainder = 0
  • Divide 404 by 202: 404 ÷ 202 : Remainder = 0
  • Divide 404 by 404: 404 ÷ 404 : Remainder = 0

Hence, Factors of 404 are 1, 2, 4, 101, 202, and 404

2. Steps to find factors of 404 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 404 using the division method, follow these steps:

  • Step 1. Start dividing 404 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 404, which is 2. Divide 404 by 2 to obtain the quotient (202).
    404 ÷ 2 = 202
  • Step 3. Repeat step 1 with the obtained quotient (202).
    202 ÷ 2 = 101
    101 ÷ 101 = 1

So, the prime factorization of 404 is, 404 = 2 x 2 x 101.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 404 as shown below:

So, the prime factorization of 404 is, 404 = 2 x 2 x 101.

3. Find factors of 404 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 404 would be the two numbers which, when multiplied, give 404 as the result.

The following table represents the calculation of factors of 404 in pairs:

Factor Pair Pair Factorization
1 and 404 1 x 404 = 404
2 and 202 2 x 202 = 404
4 and 101 4 x 101 = 404

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 404. They are called negative pair factors.

Hence, the negative pairs of 404 would be ( -1 , -404 ) , ( -2 , -202 ) and ( -4 , -101 ) .

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

  • Each number is a factor of itself. Eg. 404 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 404.
  • Every number is a factor of zero (0), since 404 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, 2, 4, 101, 202, 404 are exact divisors of 404.
  • Factors of 404 are 1, 2, 4, 101, 202, 404. Each factor divides 404 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 101, 202, 404 are all less than or equal to 404.

Frequently Asked Questions

  • What is prime factorization of 404?

    Prime factorization of 404 is 2 x 2 x 101.

  • How do you find factors of a negative number? ( eg. -404 )?

    Factors of -404 are -1, -2, -4, -101, -202, -404.

  • What are the prime factors of 404?

    The factors of 404 are 1, 2, 4, 101, 202, 404.
    Prime factors of 404 are 2, 2, 101.

  • What are pair factors of 404?

    The pair factors of 404 are (1,404), (2,202), (4,101).

  • What is the greatest prime factors of 404?

    The greatest prime factor of 404 is 101.

  • What are six multiples of 404?

    First five multiples of 404 are 808, 1212, 1616, 2020, 2424, 2828.

  • What are factors of 404?

    Factors of 404 are 1, 2, 4, 101, 202, 404.

  • Which is the smallest prime factor of 404?

    Smallest prime factor of 404 is 2.

  • Is 404 a whole number?

    Yes 404 is a whole number.

Examples of Factors

Kevin has been asked to write 5 factor(s) of 404. Can you predict the answer?

5 factor(s) of 404 are 1, 2, 4, 101, 202.

Sammy is puzzled while calculating the prime factors of 404. Can you help him find them?

Factors of 404 are 1, 2, 4, 101, 202, 404.
Prime factors of 404 are 2, 2, 101

What is prime factorization of 404?

Prime factorization of 404 is 2 x 2 x 101 = 22 x 101.

Ariel has been assigned the task to find the product of all the prime factors of 404. Can you help her?

Prime factors of 404 are 2, 2, 101.
Hence, the product of prime factors of 202.

Can you help Rubel to find out the product of the even factors of 404?

Factors of 404 are 1, 2, 4, 101, 202, 404.
Even factors of 404 are 2, 4, 202, 404.
Hence, product of even factors of 404 is; 2 x 4 x 202 x 404 = 652864.

Joy wants to calculate mean of all the factors of 404. Help him in finding the mean of 404.

Factors of 404 are 1, 2, 4, 101, 202, 404.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 404 is 1 + 2 + 4 + 101 + 202 + 404 = 714.
Hence, the mean of factors of 404 is 714 ÷ 6 = 119.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 404? Help her in writing all the factors.

Positive factors are 1, 2, 4, 101, 202, 404.
Negative factors are -1, -2, -4, -101, -202, -404.