Factors of 1920
Factors of 1920 are the list of integers that we can split evenly into 1920. It has total 32 factors of which 1920 is the biggest factor and the prime factors of 1920 are 2, 3, 5. The sum of all factors of 1920 is 6120.
- All Factors of 1920: 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 of 1920: 2, 3, 5
- Prime Factorization of 1920: 27 × 31 × 51
- Sum of Factors of 1920: 6120
1. | What Are the Factors of 1920? |
2. | Factors of 1920 by Prime Factorization |
3. | Factors of 1920 in Pairs |
4. | FAQs on Factors of 1920 |
What are Factors of 1920?
Factors of 1920 are pairs of those numbers whose products result in 1920. These factors are either prime numbers or composite numbers.
How to Find the Factors of 1920?
To find the factors of 1920, we will have to find the list of numbers that would divide 1920 without leaving any remainder.
- 1920/40 = 48; therefore, 40 is a factor of 1920 and 48 is also a factor of 1920.
- 1920/64 = 30; therefore, 64 is a factor of 1920 and 30 is also a factor of 1920.
☛ Also Check:
- Factors of 17 - The factors of 17 are 1, 17
- Factors of 37 - The factors of 37 are 1, 37
- Factors of 15 - The factors of 15 are 1, 3, 5, 15
- Factors of 22 - The factors of 22 are 1, 2, 11, 22
- Factors of 5 - The factors of 5 are 1, 5
Factors of 1920 by Prime Factorization
- 1920 ÷ 2 = 960
- 960 ÷ 2 = 480
- 480 ÷ 2 = 240
- 240 ÷ 2 = 120
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
Further dividing 15 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 15 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 1920 can be written as 27 × 31 × 51 where 2, 3, 5 are prime.
Factors of 1920 in Pairs
Pair factors of 1920 are the pairs of numbers that when multiplied give the product 1920. The factors of 1920 in pairs are:
- 1 × 1920 = (1, 1920)
- 2 × 960 = (2, 960)
- 3 × 640 = (3, 640)
- 4 × 480 = (4, 480)
- 5 × 384 = (5, 384)
- 6 × 320 = (6, 320)
- 8 × 240 = (8, 240)
- 10 × 192 = (10, 192)
- 12 × 160 = (12, 160)
- 15 × 128 = (15, 128)
- 16 × 120 = (16, 120)
- 20 × 96 = (20, 96)
- 24 × 80 = (24, 80)
- 30 × 64 = (30, 64)
- 32 × 60 = (32, 60)
- 40 × 48 = (40, 48)
Negative pair factors of 1920 are:
- -1 × -1920 = (-1, -1920)
- -2 × -960 = (-2, -960)
- -3 × -640 = (-3, -640)
- -4 × -480 = (-4, -480)
- -5 × -384 = (-5, -384)
- -6 × -320 = (-6, -320)
- -8 × -240 = (-8, -240)
- -10 × -192 = (-10, -192)
- -12 × -160 = (-12, -160)
- -15 × -128 = (-15, -128)
- -16 × -120 = (-16, -120)
- -20 × -96 = (-20, -96)
- -24 × -80 = (-24, -80)
- -30 × -64 = (-30, -64)
- -32 × -60 = (-32, -60)
- -40 × -48 = (-40, -48)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 1920 Solved Examples
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Example 1: How many factors are there for 1920?
Solution:
The factors of 1920 are too many, therefore if we can find the prime factorization of 1920, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).
Prime Factorization of 1920 = 27 × 31 × 51
Therefore, the total number of factors are (7 + 1) × (1 + 1) × (1 + 1) = 8 × 2 × 2 = 32 -
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1920 and 351.
Solution:
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, 1920 and factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351.
Therefore, the Least Common Multiple (LCM) of 1920 and 351 is 224640 and Greatest Common Divisor (GCD) of 1920 and 351 is 3. -
Example 3: Find if 5, 8, 10, 15, 16, 192, 320 and 757 are factors of 1920.
Solution:
When we divide 1920 by 757 it leaves a remainder. Therefore, the number 757 is not a factor of 1920. All numbers except 757 are factors of 1920.
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Example 4: Find the product of all the prime factors of 1920.
Solution:
Since, the prime factors of 1920 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 1920
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, 1920 and its negative factors 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.
What is the Sum of the Factors of 1920?
Sum of all factors of 1920 = (27 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 6120
What are the Pair Factors of 1920?
The pair factors of 1920 are (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).
What is the Greatest Common Factor of 1920 and 978?
The factors of 1920 and 978 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 and 1, 2, 3, 6, 163, 326, 489, 978 respectively.
Common factors of 1920 and 978 are [1, 2, 3, 6].
Hence, the Greatest Common Factor (GCF) of 1920 and 978 is 6.
What are the Common Factors of 1920 and 282?
Since, 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, 1920 and the factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282.
Hence, [1, 2, 3, 6] are the common factors of 1920 and 282.
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