1. Steps to find factors of 384 using Division Method

Example: Find factors of 384

  • Divide 384 by 1: 384 ÷ 1 : Remainder = 0
  • Divide 384 by 2: 384 ÷ 2 : Remainder = 0
  • Divide 384 by 3: 384 ÷ 3 : Remainder = 0
  • Divide 384 by 4: 384 ÷ 4 : Remainder = 0
  • Divide 384 by 6: 384 ÷ 6 : Remainder = 0
  • Divide 384 by 8: 384 ÷ 8 : Remainder = 0
  • Divide 384 by 12: 384 ÷ 12 : Remainder = 0
  • Divide 384 by 16: 384 ÷ 16 : Remainder = 0
  • Divide 384 by 24: 384 ÷ 24 : Remainder = 0
  • Divide 384 by 32: 384 ÷ 32 : Remainder = 0
  • Divide 384 by 48: 384 ÷ 48 : Remainder = 0
  • Divide 384 by 64: 384 ÷ 64 : Remainder = 0
  • Divide 384 by 96: 384 ÷ 96 : Remainder = 0
  • Divide 384 by 128: 384 ÷ 128 : Remainder = 0
  • Divide 384 by 192: 384 ÷ 192 : Remainder = 0
  • Divide 384 by 384: 384 ÷ 384 : Remainder = 0

Hence, Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, and 384

2. Steps to find factors of 384 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 384 using the division method, follow these steps:

  • Step 1. Start dividing 384 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 384, which is 2. Divide 384 by 2 to obtain the quotient (192).
    384 ÷ 2 = 192
  • Step 3. Repeat step 1 with the obtained quotient (192).
    192 ÷ 2 = 96
    96 ÷ 2 = 48
    48 ÷ 2 = 24
    24 ÷ 2 = 12
    12 ÷ 2 = 6
    6 ÷ 2 = 3
    3 ÷ 3 = 1

So, the prime factorization of 384 is, 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 384 as shown below:

So, the prime factorization of 384 is, 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.

3. Find factors of 384 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 384 would be the two numbers which, when multiplied, give 384 as the result.

The following table represents the calculation of factors of 384 in pairs:

Factor Pair Pair Factorization
1 and 384 1 x 384 = 384
2 and 192 2 x 192 = 384
3 and 128 3 x 128 = 384
4 and 96 4 x 96 = 384
6 and 64 6 x 64 = 384
8 and 48 8 x 48 = 384
12 and 32 12 x 32 = 384
16 and 24 16 x 24 = 384

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 384. They are called negative pair factors.

Hence, the negative pairs of 384 would be ( -1 , -384 ) , ( -2 , -192 ) , ( -3 , -128 ) , ( -4 , -96 ) , ( -6 , -64 ) , ( -8 , -48 ) , ( -12 , -32 ) and ( -16 , -24 ) .

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. 384 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 384.
  • Every number is a factor of zero (0), since 384 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, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384 are exact divisors of 384.
  • Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384. Each factor divides 384 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384 are all less than or equal to 384.

Frequently Asked Questions

  • How do you find factors of a negative number? ( eg. -384 )?

    Factors of -384 are -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, -128, -192, -384.

  • What is the sum of all factors of 384?

    The sum of all factors of 384 is 1020.

  • What is prime factorization of 384?

    Prime factorization of 384 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3.

  • What are the pair factors of 384?

    Pair factors of 384 are (1,384), (2,192), (3,128), (4,96), (6,64), (8,48), (12,32), (16,24).

  • What are six multiples of 384?

    First five multiples of 384 are 768, 1152, 1536, 1920, 2304, 2688.

  • Is 384 a whole number?

    Yes 384 is a whole number.

  • Which is the smallest prime factor of 384?

    Smallest prime factor of 384 is 2.

  • What are five multiples of 384?

    First five multiples of 384 are 768, 1152, 1536, 1920, 2304.

  • Write all factors of 384?

    Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.

Examples of Factors

Joey wants to write all the prime factors of 384 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 384 are 2, 2, 2, 2, 2, 2, 2, 3.
So in exponential form it can be written as 27 x 3.

How many factors are there for 384?

Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 384. Can you predict the answer?

15 factor(s) of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192.

Sammy is puzzled while calculating the prime factors of 384. Can you help him find them?

Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
Prime factors of 384 are 2, 2, 2, 2, 2, 2, 2, 3

What is prime factorization of 384?

Prime factorization of 384 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 27 x 3.

Ariel has been assigned the task to find the product of all the prime factors of 384. Can you help her?

Prime factors of 384 are 2, 2, 2, 2, 2, 2, 2, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 384?

Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
Even factors of 384 are 2, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
Hence, product of even factors of 384 is; 2 x 4 x 6 x 8 x 12 x 16 x 24 x 32 x 48 x 64 x 96 x 128 x 192 x 384 = 157589958160948400000.