250 LearnersLast updated on May 26th, 2025
Factors of 1920
Factors of 1920 are numbers that can divide 1920 completely without any remainder. We often use factors in various aspects of life, such as organizing items, managing events, or solving mathematical problems. In this topic, we will explore the factors of 1920 and the different methods to find them.
What are the Factors of 1920?
The factors of 1920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, and 1920.
Positive Factors: The positive factors of 1920 include all the above numbers.
Negative Factors: The negative factors are the negative counterparts of the positive factors:
-1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -128, -160, -192, -240, -320, -384, -480, -640, -960, -1920.
Prime Factors: Prime factors are the prime numbers that multiply together to give 1920 as the product.
Prime factors of 1920: 2, 3, 5.
Prime Factorization: Prime factorization involves breaking down 1920 into its prime factors.
It is expressed as 27 × 31 × 52
|
Positive Factors |
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920 |
|
Negative Factors |
-1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -64, -80, -96, -120, -128, -160, -192, -240, -320, -384, -480, -640, -960, -1920 |
|
Prime Factors |
2, 3, 5 |
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Prime Factorization |
27 × 31 × 51 |
This breakdown helps in understanding the various factors of 1920, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 1920?
There are different methods to find the factors of 1920. They are mentioned below.
Methods to Find the Factors of 1920:
- Multiplication Method
- Division Method
- Prime Factors and Prime Factorization
- Factor Tree
Finding Factors Using the Multiplication Method
The multiplication method finds pairs of factors that give 1920 as their product.
Steps:
Step 1: Find pairs of numbers whose product is 1920.
Step 2: The factors are the numbers that multiply to give 1920.
Step 3: List all pairs of numbers.
Factor Pairs of 1920:
- 1 × 1920 = 1920
- 2 × 960 = 1920
- 3 × 640 = 1920
- 4 × 480 = 1920
- 5 × 384 = 1920
- 6 × 320 = 1920
- 8 × 240 = 1920
- 10 × 192 = 1920
- 12 ×160 = 1920
- 15 × 128 = 1920
- 16 ×120 = 1920
- 20 × 96 = 1920
- 24 × 80 = 1920
- 30 × 64 = 1920
- 32 × 60 = 1920
- 40 × 48 = 1920
Thus, the factors of 1920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 384, 480, 640, 960, and 1920.
Finding Factors Using the Division Method
The division method identifies numbers that completely divide 1920.
Step 1: Start with 1 (since every number is divisible by 1).
Example: 1920÷1=1920.
Step 2: Move to the next integer. Continue dividing and noting numbers that divide evenly.
Thus, the factors of 1920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, and 1920.
Prime Factors and Prime Factorization
Prime Factors: The prime numbers 2,3, and 5 are factors of 1920.
Prime Factorization Steps:
Step 1: Divide 1920 by the smallest prime number, 2:
1920÷2=960
Step 2:Repeat division by 222 until it no longer divides:
960÷2=480, 480÷2=240, and so on.
Step 3: Continue with the next smallest primes, 333 and 555.
Prime factorization: 27 × 31 × 51
Factor Tree
A factor tree visually represents the prime factorization process for 1920. Each branch splits into prime factors until only prime numbers remain.
This tree shows the breakdown of 1920 into its prime factors: 2 × 5 × 13.
Positive and Negative Factor Pairs of 1920
Factors of 1920 can be written in both positive and negative pairs. These pairs multiply to give the number 1920.
Positive Factor Pairs:
(1, 1920), (2, 960), (3, 640), (4, 480), (5, 384), (6, 320), (8, 240), (10, 192), (12, 160), (15, 128), (16, 120), (20, 96), (24, 80), (30, 64), (32, 60), (40, 48).
Negative Factor Pairs:
(-1, -1920), (-2, -960), (-3, -640), (-4, -480), (-5, -384), (-6, -320), (-8, -240), (-10, -192), (-12, -160), (-15, -128), (-16, -120), (-20, -96), (-24, -80), (-30, -64), (-32, -60), (-40, -48).
Common Mistakes and How to Avoid Them for Factors of 1920
Mistakes can happen when finding the factors of 1920. Below are some common errors and tips on how to avoid them for accurate factor identification.
Mistake 1
Assuming only small numbers as factors.
Remember to find both small and large numbers that divide 1920 completely.
Factors of 1920 Examples
Problem 1
Can you identify the factors of 1920?
Factors of 1920 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920.
Explanation
To find the factors of 1920, divide it by numbers up to its square root. Include both divisors whenever the division results in no remainder.
Problem 2
Verify whether 1920 is a multiple of 11
No, 1920 is not a multiple of 11.
Explanation
A number is a multiple of another if it can be divided evenly by it. Dividing 1920 by 11 leaves a remainder, confirming it is not a multiple of 11.
Problem 3
Identify the perfect square from the factors of 1920
The perfect square factors of 1920 are 1, 4, 16, and 64
Explanation
A perfect square is obtained by multiplying a number by itself. Among the factors of 1920, 1 (1×1), 4 (2×2), 16 (4×4), and 64 (8×8) qualify as perfect squares.
Problem 4
Can you check whether 1920 and 64 are co-prime?
No, 1920 and 64 are not co-prime.
Explanation
Co-prime numbers have no common factors other than 1. Factors of 1920 include 64, so their GCF is 64, not 1. Hence, they are not co-prime.
Problem 5
Is 1920 divisible by 9?
No, 1920 is not divisible by 9.
Explanation
A number is divisible by 9 if the sum of its digits is a multiple of 9. The sum of the digits of 1920 is 1+9+2+0 = 12, which is not a multiple of 9.
FAQs on Factors of 1920
1.What are the factors of 1920?
2.How do you determine if a number is a factor of 1920?
3.What is the smallest factor of 1920?
4.What is the largest factor of 1920?
5.How many factors does 1920 have?
6.How many odd factors does 1920 have?
7.What factors go into 1920?
8.Do any perfect squares exist in the factors of 1920?
Important Glossaries for the Factors of 1920
- Factor: A number that divides another number completely without leaving any remainder.Example: Factors of 1920 are 1, 2, 3, etc.
- Prime Factorization: The process of breaking a number down into its smallest prime number components. Example: Prime factorization of 1920 is 27×31×51.
- Perfect Square: A number that results from multiplying an integer by itself. Example: Perfect square factors of 1920 include 1, 4, 16, and 64.
- Factor Pair: A pair of numbers that, when multiplied, give the original number. Example: One-factor pair of 1920 is (30, 64).
- Composite Number: A number with more than two factors. Example: 1920 is a composite number, as it has multiple factors beyond 1 and itself.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
