Factors of 9520
Factors of 9520 are the list of integers that we can split evenly into 9520. There are overall 40 factors of 9520 among which 9520 is the biggest factor and its prime factors are 2, 5, 7, 17. The Prime Factorization of 9520 is 24 × 51 × 71 × 171.
- All Factors of 9520: 1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 28, 34, 35, 40, 56, 68, 70, 80, 85, 112, 119, 136, 140, 170, 238, 272, 280, 340, 476, 560, 595, 680, 952, 1190, 1360, 1904, 2380, 4760 and 9520
- Prime Factors of 9520: 2, 5, 7, 17
- Prime Factorization of 9520: 24 × 51 × 71 × 171
- Sum of Factors of 9520: 26784
1. | What Are the Factors of 9520? |
2. | Factors of 9520 by Prime Factorization |
3. | Factors of 9520 in Pairs |
4. | FAQs on Factors of 9520 |
![Factors of 9520](https://static.qumath.in/static/website/old-cdn-static/factors/factors-of-9520.png)
What are Factors of 9520?
Factors of 9520 are pairs of those numbers whose products result in 9520. These factors are either prime numbers or composite numbers.
How to Find the Factors of 9520?
To find the factors of 9520, we will have to find the list of numbers that would divide 9520 without leaving any remainder.
- 9520/4760 = 2; therefore, 4760 is a factor of 9520 and 2 is also a factor of 9520.
- 9520/952 = 10; therefore, 952 is a factor of 9520 and 10 is also a factor of 9520.
☛ Also Check:
- Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
- Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 33 - The factors of 33 are 1, 3, 11, 33
- Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 37 - The factors of 37 are 1, 37
Factors of 9520 by Prime Factorization
- 9520 ÷ 2 = 4760
- 4760 ÷ 2 = 2380
- 2380 ÷ 2 = 1190
- 1190 ÷ 2 = 595
Further dividing 595 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 595 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 9520 can be written as 24 × 51 × 71 × 171 where 2, 5, 7, 17 are prime.
Factors of 9520 in Pairs
Pair factors of 9520 are the pairs of numbers that when multiplied give the product 9520. The factors of 9520 in pairs are:
- 1 × 9520 = (1, 9520)
- 2 × 4760 = (2, 4760)
- 4 × 2380 = (4, 2380)
- 5 × 1904 = (5, 1904)
- 7 × 1360 = (7, 1360)
- 8 × 1190 = (8, 1190)
- 10 × 952 = (10, 952)
- 14 × 680 = (14, 680)
- 16 × 595 = (16, 595)
- 17 × 560 = (17, 560)
- 20 × 476 = (20, 476)
- 28 × 340 = (28, 340)
- 34 × 280 = (34, 280)
- 35 × 272 = (35, 272)
- 40 × 238 = (40, 238)
- 56 × 170 = (56, 170)
- 68 × 140 = (68, 140)
- 70 × 136 = (70, 136)
- 80 × 119 = (80, 119)
- 85 × 112 = (85, 112)
Negative pair factors of 9520 are:
- -1 × -9520 = (-1, -9520)
- -2 × -4760 = (-2, -4760)
- -4 × -2380 = (-4, -2380)
- -5 × -1904 = (-5, -1904)
- -7 × -1360 = (-7, -1360)
- -8 × -1190 = (-8, -1190)
- -10 × -952 = (-10, -952)
- -14 × -680 = (-14, -680)
- -16 × -595 = (-16, -595)
- -17 × -560 = (-17, -560)
- -20 × -476 = (-20, -476)
- -28 × -340 = (-28, -340)
- -34 × -280 = (-34, -280)
- -35 × -272 = (-35, -272)
- -40 × -238 = (-40, -238)
- -56 × -170 = (-56, -170)
- -68 × -140 = (-68, -140)
- -70 × -136 = (-70, -136)
- -80 × -119 = (-80, -119)
- -85 × -112 = (-85, -112)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 9520 Solved Examples
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Example 1: How many factors are there for 9520?
Solution:
The factors of 9520 are too many, therefore if we can find the prime factorization of 9520, 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 9520 = 24 × 51 × 71 × 171
Therefore, the total number of factors are (4 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 5 × 2 × 2 × 2 = 40 -
Example 2: Find the LCM and Greatest Common Divisor (GCD) of 9520 and 8276.
Solution:
The factors of 9520 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 28, 34, 35, 40, 56, 68, 70, 80, 85, 112, 119, 136, 140, 170, 238, 272, 280, 340, 476, 560, 595, 680, 952, 1190, 1360, 1904, 2380, 4760, 9520 and factors of 8276 are 1, 2, 4, 2069, 4138, 8276.
Therefore, the LCM of 9520 and 8276 is 19696880 and Greatest Common Divisor (GCD) of 9520 and 8276 is 4. -
Example 3: Find if 1, 7, 28, 119, 952, 1190, 2380 and 4065 are factors of 9520.
Solution:
When we divide 9520 by 4065 it leaves a remainder. Therefore, the number 4065 is not a factor of 9520. All numbers except 4065 are factors of 9520.
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Example 4: Find the product of all the prime factors of 9520.
Solution:
Since, the prime factors of 9520 are 2, 5, 7, 17. Therefore, the product of prime factors = 2 × 5 × 7 × 17 = 1190.
FAQs on Factors of 9520
What are the Factors of 9520?
The factors of 9520 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 28, 34, 35, 40, 56, 68, 70, 80, 85, 112, 119, 136, 140, 170, 238, 272, 280, 340, 476, 560, 595, 680, 952, 1190, 1360, 1904, 2380, 4760, 9520 and its negative factors are -1, -2, -4, -5, -7, -8, -10, -14, -16, -17, -20, -28, -34, -35, -40, -56, -68, -70, -80, -85, -112, -119, -136, -140, -170, -238, -272, -280, -340, -476, -560, -595, -680, -952, -1190, -1360, -1904, -2380, -4760, -9520.
What is the Sum of all the Factors of 9520?
Sum of all factors of 9520 = (24 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (171 + 1 - 1)/(17 - 1) = 26784
What Numbers are the Prime Factors of 9520?
The prime factors of 9520 are 2, 5, 7, 17.
What is the Greatest Common Factor of 9520 and 3587?
The factors of 9520 and 3587 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 28, 34, 35, 40, 56, 68, 70, 80, 85, 112, 119, 136, 140, 170, 238, 272, 280, 340, 476, 560, 595, 680, 952, 1190, 1360, 1904, 2380, 4760, 9520 and 1, 17, 211, 3587 respectively.
Common factors of 9520 and 3587 are [1, 17].
Hence, the Greatest Common Factor of 9520 and 3587 is 17.
How Many Factors of 9520 are also common to the Factors of 5873?
Since, the factors of 9520 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 28, 34, 35, 40, 56, 68, 70, 80, 85, 112, 119, 136, 140, 170, 238, 272, 280, 340, 476, 560, 595, 680, 952, 1190, 1360, 1904, 2380, 4760, 9520 and the factors of 5873 are 1, 7, 839, 5873.
Hence, [1, 7] are the common factors of 9520 and 5873.
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