How to finds the factors of 384?

factors of 384

How to finds the factors of 384

factors of 384

Welcome, dear readers, to another interactive blog where we embark on a mathematical journey to unravel the factors of the number 384. Whether you’re a student striving to master the art of factoring or a curious mind seeking a deeper understanding, you’re in the right place. Let’s dive into the fascinating world of numbers and discover the factors of 384.

Understanding Factors of 384

In mathematics, factors are numbers that divide another number without leaving a remainder. For the number 280, let’s explore the methods to identify its factors.

Method 1: Trial Division method to find factors of 384

Factors of 384

Factors of 384 can be found by ckecking the divisibility of 384 by the whole numbers 1 through 384 ≈ 19.60. If a whole number divides 384 exactly, both

  • the number itself and
  • the result of the division by that number

are the factors of 384.

    • 384 is divisible by 2. Write 2 to the left. When 384 is divided by 2 the result is 192. Write 192 under 384
    • 192 is divisible by 2. Write 2 to the left. When 192 is divided by 2 the result is 96. Write 96 under 192
    • 96 is divisible by 2. Write 2 to the left. When 96 is divided by 2 the result is 48. Write 48 under 96
    • 48 is divisible by 2. Write 2 to the left. When 48 is divided by 2 the result is 24. Write 24 under 48
    • 24 is divisible by 2. Write 2 to the left. When 24 is divided by 2 the result is 12. Write 12 under 24
    • 12 is divisible by 2. Write 2 to the left. When 12 is divided by 2 the result is 6. Write 6 under 12
    • 6 is divisible by 2. Write 2 to the left. When 6 is divided by 2 the result is 3. Write 3 under 6
    • 3 is divisible by 3. Write 3 to the left. When 3 is divided by 3 the result is 1. Write 1 under 3
Upside Division factors of 384

Method 2: Pair Factors of 384

factors pairs of 384

To begin our investigation, let’s use a simple approach: listing factors in pairs. Suppose you are opening a box and you start with 1 and the number itself, and you gradually open up factors in pairs until you get to the middle. This practical method is similar to finding the ingredients in a recipe with mathematics.

Pair Factors of 384:

384 has 16 factors.

Factors:

12346812162432486496128192384

Factor Pairs:

  • 1 × 384 = 384
  • 2 × 192 = 384
  • 3 × 128 = 384
  • 4 × 96 = 384
  • 6 × 64 = 384
  • 8 × 48 = 384
  • 12 × 32 = 384
  • 16 × 24 = 384

Positive and Negative Factors

Positive Factors

Factor PairsProduct
1, 384384
2, 192384
3, 128384
4, 96384

Negative Factors

Factor PairsProduct
-1, -384384
-2, -192384
-3, -128384
-4, -96384

Calculating Prime Factors

prime factors of 384

Prime factors are the building blocks of a number. They are the prime numbers that multiply to give the original number.

Prime Factors of 384:

384 = 2 × 2 × 2 × 2 × 2 × 2 × 2 ×3 

384 = 27 × 3

Factors Tree

A factors tree is a visual representation of the prime factorization of a number.

Factors tree of 384

Practice Questions for factors of 280

  1. If a rectangular garden has an area of 384 square meters and a length of 24 meters, what is its width?
  2. In a group of 384 students, if they are arranged in rows of 12, how many rows are there?
  3. A factory produces 384 widgets in a day. If each box contains 16 widgets, how many boxes are produced in a day?
  4. An investor deposits $384 in a bank account that offers an annual interest rate of 8%. How much interest will be earned after one year?
  5. The perimeter of a rectangular field is 384 meters. If the length is 96 meters, what is the width of the field?

FAQs about factors of 280

Q: Can I use the prime factorization to find common factors or multiples of 384 with other numbers?

A: Absolutely! The prime factorization is a powerful tool for finding common factors and multiples. Compare the prime factorizations of different numbers to find their relationships.

Q: Are there any shortcuts for finding factors, especially for larger numbers like 384?

A: While no universal shortcut exists, understanding divisibility rules for small prime numbers can make the process quicker. Additionally, recognizing patterns in factor pairs can be helpful.

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