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Factors of 384

384 is the sum of a twin prime pair (191 + 193). It could also be expressed as the sum of six consecutive prime numbers (53 + 59 + 61 + 67 + 71 + 73). In this lesson, let us calculate the factors of 384, prime factors of 384, and factors of 384 in pairs along with the solved examples for a better understanding.

  • Factors of 384: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, and 384
  • Prime Factorization of 384 : 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 27 × 3 
1. What Are the Factors of 384?
2. How to Calculate the Factors of 384?
3. Factors of 384 by Prime Factorization
4. Factors of 384 in Pairs
5. FAQs on Factors of 384

What Are the Factors of 384?

All the numbers that divide 384 completely, leaving no remainder, are the factors of 384.  The numbers 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, and 384 divide 384 without any remainder. 

How to Calculate the Factors of 384?

Method 1: Using the divisibilty rules,

  • Check for the divisibility of 384 by 1, 2, 3, 5, 6, and so on. All the numbers that pass the divisibilty tests are the factors of 384.
  • The quotient obtained are also the factors of 384. Thus we have 16 factors in all.
384 ÷ 1 = 384
384 ÷ 2 = 192
384 ÷ 3 = 128
384 ÷ 4 = 96
384 ÷ 6 = 64
384 ÷ 8 = 48
384 ÷ 12 = 32
384 ÷ 16 = 24

Method 2 : Using prime factorization,

factor tree of 384- prime factors of 384

  • Find all the prime factors using factor tree and evaluate the composite factors of 384. We obtain the prime factorization of 384 as 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 2 7  × 3
  • Find all the possible combinations of these seven 2s and one 3  to multiply and get the product to evaluate all the composite factors. Thus we obtain all the 16 factors.
2  2 × 3 = 6
2 × 2 = 4 2 × 2 × 3 = 12
2 × 2 × 2 = 8 2 × 2 × 2 × 3 = 24
2 × 2 × 2 × 2 = 16 2 × 2 × 2 × 2 × 3 = 48
2 × 2 × 2 × 2 × 2 = 32 2 × 2 × 2 × 2 × 2 × 3 = 96
2 × 2 × 2 × 2 × 2 × 2 = 64 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192
2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 384

Explore factors using illustrations and interactive examples

  • Factors of 512: The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, and 512.
  • Factors of 175: The factors of 175 are 1, 5, 7, 25, 35, and 175.
  • Factors of 320:  The factors of 729 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160 and 320
  • Factors of 216: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
  • Factors of 112: The factors of 112 are  1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.

Factors of 384 by Prime Factorization

Prime factorization is expressing a number as a product of its factors.

Prime factorization of 384

  • We determine the prime factors using the division method or the factor tree method. 
  • 384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 = 27 × 3.
  • Considering the exponents alone, add 1 to each and multiply them.
  • The product obtained so helps in determining the total number of factors of 384. Here it is (7+1) × (1+1) = 8 × 2 = 16 factors.

Factors of 384 in Pairs

Factor pairs are the numbers which give the number 384 when multipled together. Number 1 × Number 2 = 384. This is expressed as factors of 384 in ordered pairs as (number 1, number2). We have 8 such factor pairs of 384 as observed in the pattern below. The distinct factor pairs of 384 are (1, 384), (2, 192), (3,128), (4, 96), (6, 64), (8,48), (12,32), and (16,24).

Important Notes

  • The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, and 384
  • The prime factors of 384 are 2 and 3. 
  • The prime factorization is 27 × 3.

Challenging Questions

  • The number of men and women who attend a conference is given as 540 and 384 respectively. Each row should have equal number of people. Only men or women will be in each row. What is the greatest number of people that could be in each row?
  • How do you differentiate the factors of 384 from the multiples of 384?
 

Factors of 384 Solved Examples

  1. Example 1: 384 tourists go canoeing at a camp. No more than 4 tourists are allowed in each canoe. What is the minimum number of canoes needed for all the tourists to go canoeing?

    Solution:

    4 tourists × number of canoes = 384 tourists

    4 × _____  = 384

    Finding the missing pair factor of 4, we do 384 ÷ 4 = 96

    Thus the minimum number of canoes needed = 96.

  2. Example 2: Candies come in packages of 16. Stephie got 384 candies. How many packages did she buy? 

    Solution: Number of packages × 16 candies = 384 candies

    _____ × 16 = 384

    Finding the missing factor pair, we get 384 ÷ 16 = 24

    Thus Stephie bought 24 packages.

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FAQs on Factors of 384

What are the factors of 384?

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

What are the common factors of 384 and 324?

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

The factors of 324 are  1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.

The common factors of 384 and 324 are 1, 2, 3, 4, 6, and 12.

What are the factors of 384 that add up to 80 ?

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

Among these, 16 and 64 sum up to 80.

What are the total number of factors of 384?

There are 16 factors of 384 in all. 

What are the prime factors of 384?

2 and 3 are the prime factors of 384.

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