1. Steps to find factors of 304 using Division Method

Example: Find factors of 304

  • Divide 304 by 1: 304 ÷ 1 : Remainder = 0
  • Divide 304 by 2: 304 ÷ 2 : Remainder = 0
  • Divide 304 by 4: 304 ÷ 4 : Remainder = 0
  • Divide 304 by 8: 304 ÷ 8 : Remainder = 0
  • Divide 304 by 16: 304 ÷ 16 : Remainder = 0
  • Divide 304 by 19: 304 ÷ 19 : Remainder = 0
  • Divide 304 by 38: 304 ÷ 38 : Remainder = 0
  • Divide 304 by 76: 304 ÷ 76 : Remainder = 0
  • Divide 304 by 152: 304 ÷ 152 : Remainder = 0
  • Divide 304 by 304: 304 ÷ 304 : Remainder = 0

Hence, Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, and 304

2. Steps to find factors of 304 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 304 using the division method, follow these steps:

  • Step 1. Start dividing 304 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 304, which is 2. Divide 304 by 2 to obtain the quotient (152).
    304 ÷ 2 = 152
  • Step 3. Repeat step 1 with the obtained quotient (152).
    152 ÷ 2 = 76
    76 ÷ 2 = 38
    38 ÷ 2 = 19
    19 ÷ 19 = 1

So, the prime factorization of 304 is, 304 = 2 x 2 x 2 x 2 x 19.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 304 as shown below:

So, the prime factorization of 304 is, 304 = 2 x 2 x 2 x 2 x 19.

3. Find factors of 304 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 304 would be the two numbers which, when multiplied, give 304 as the result.

The following table represents the calculation of factors of 304 in pairs:

Factor Pair Pair Factorization
1 and 304 1 x 304 = 304
2 and 152 2 x 152 = 304
4 and 76 4 x 76 = 304
8 and 38 8 x 38 = 304
16 and 19 16 x 19 = 304

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 304. They are called negative pair factors.

Hence, the negative pairs of 304 would be ( -1 , -304 ) , ( -2 , -152 ) , ( -4 , -76 ) , ( -8 , -38 ) and ( -16 , -19 ) .

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. 304 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 304.
  • Every number is a factor of zero (0), since 304 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, 8, 16, 19, 38, 76, 152, 304 are exact divisors of 304.
  • Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304. Each factor divides 304 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 16, 19, 38, 76, 152, 304 are all less than or equal to 304.

Frequently Asked Questions

  • Which is the smallest prime factor of 304?

    The smallest prime factor of 304 is 2.

  • Is 304 a whole number?

    Yes 304 is a whole number.

  • What are the prime factors of 304?

    The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304.
    Prime factors of 304 are 2, 2, 2, 2, 19.

  • What two numbers make 304?

    Two numbers that make 304 are 2 and 152.

  • What are multiples of 304?

    First five multiples of 304 are 608, 912, 1216, 1520.

  • What is the sum of all factors of 304?

    The sum of all factors of 304 is 620.

  • What are five multiples of 304?

    First five multiples of 304 are 608, 912, 1216, 1520, 1824.

  • Is 304 a perfect square?

    No 304 is not a perfect square.

  • What is the greatest prime factors of 304?

    The greatest prime factor of 304 is 19.

Examples of Factors

How many factors are there for 304?

Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304.
So there are in total 10 factors.

Kevin has been asked to write 9 factor(s) of 304. Can you predict the answer?

9 factor(s) of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152.

Sammy is puzzled while calculating the prime factors of 304. Can you help him find them?

Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304.
Prime factors of 304 are 2, 2, 2, 2, 19

What is prime factorization of 304?

Prime factorization of 304 is 2 x 2 x 2 x 2 x 19 = 24 x 19.

Ariel has been assigned the task to find the product of all the prime factors of 304. Can you help her?

Prime factors of 304 are 2, 2, 2, 2, 19.
Hence, the product of prime factors of 38.

Can you help Rubel to find out the product of the even factors of 304?

Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304.
Even factors of 304 are 2, 4, 8, 16, 38, 76, 152, 304.
Hence, product of even factors of 304 is; 2 x 4 x 8 x 16 x 38 x 76 x 152 x 304 = 136651472896.

Joy wants to calculate mean of all the factors of 304. Help him in finding the mean of 304.

Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 304 is 1 + 2 + 4 + 8 + 16 + 19 + 38 + 76 + 152 + 304 = 620.
Hence, the mean of factors of 304 is 620 ÷ 10 = 62.00.