Factors of 9000
Factors of 9000 are the list of integers that we can split evenly into 9000. There are 48 factors of 9000 of which 9000 itself is the biggest factor and its prime factors are 2, 3, 5 The sum of all factors of 9000 is 30420.
 All Factors of 9000: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500 and 9000
 Prime Factors of 9000: 2, 3, 5
 Prime Factorization of 9000: 2^{3} × 3^{2} × 5^{3}
 Sum of Factors of 9000: 30420
1.  What Are the Factors of 9000? 
2.  Factors of 9000 by Prime Factorization 
3.  Factors of 9000 in Pairs 
4.  FAQs on Factors of 9000 
What are Factors of 9000?
Factors of 9000 are pairs of those numbers whose products result in 9000. These factors are either prime numbers or composite numbers.
How to Find the Factors of 9000?
To find the factors of 9000, we will have to find the list of numbers that would divide 9000 without leaving any remainder.
 9000/45 = 200; therefore, 45 is a factor of 9000 and 200 is also a factor of 9000.
 9000/10 = 900; therefore, 10 is a factor of 9000 and 900 is also a factor of 9000.
☛ Also Check:
 Factors of 32  The factors of 32 are 1, 2, 4, 8, 16, 32
 Factors of 13  The factors of 13 are 1, 13
 Factors of 17  The factors of 17 are 1, 17
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
 Factors of 63  The factors of 63 are 1, 3, 7, 9, 21, 63
Factors of 9000 by Prime Factorization
 9000 ÷ 2 = 4500
 4500 ÷ 2 = 2250
 2250 ÷ 2 = 1125
Further dividing 1125 by 2 gives a nonzero remainder. So we stop the process and continue dividing the number 1125 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 9000 can be written as 2^{3} × 3^{2} × 5^{3} where 2, 3, 5 are prime.
Factors of 9000 in Pairs
Pair factors of 9000 are the pairs of numbers that when multiplied give the product 9000. The factors of 9000 in pairs are:
 1 × 9000 = (1, 9000)
 2 × 4500 = (2, 4500)
 3 × 3000 = (3, 3000)
 4 × 2250 = (4, 2250)
 5 × 1800 = (5, 1800)
 6 × 1500 = (6, 1500)
 8 × 1125 = (8, 1125)
 9 × 1000 = (9, 1000)
 10 × 900 = (10, 900)
 12 × 750 = (12, 750)
 15 × 600 = (15, 600)
 18 × 500 = (18, 500)
 20 × 450 = (20, 450)
 24 × 375 = (24, 375)
 25 × 360 = (25, 360)
 30 × 300 = (30, 300)
 36 × 250 = (36, 250)
 40 × 225 = (40, 225)
 45 × 200 = (45, 200)
 50 × 180 = (50, 180)
 60 × 150 = (60, 150)
 72 × 125 = (72, 125)
 75 × 120 = (75, 120)
 90 × 100 = (90, 100)
Negative pair factors of 9000 are:
 1 × 9000 = (1, 9000)
 2 × 4500 = (2, 4500)
 3 × 3000 = (3, 3000)
 4 × 2250 = (4, 2250)
 5 × 1800 = (5, 1800)
 6 × 1500 = (6, 1500)
 8 × 1125 = (8, 1125)
 9 × 1000 = (9, 1000)
 10 × 900 = (10, 900)
 12 × 750 = (12, 750)
 15 × 600 = (15, 600)
 18 × 500 = (18, 500)
 20 × 450 = (20, 450)
 24 × 375 = (24, 375)
 25 × 360 = (25, 360)
 30 × 300 = (30, 300)
 36 × 250 = (36, 250)
 40 × 225 = (40, 225)
 45 × 200 = (45, 200)
 50 × 180 = (50, 180)
 60 × 150 = (60, 150)
 72 × 125 = (72, 125)
 75 × 120 = (75, 120)
 90 × 100 = (90, 100)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 9000 Solved Examples

Example 1: How many factors are there for 9000?
Solution:
The factors of 9000 are too many, therefore if we can find the prime factorization of 9000, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^{x} × b^{y} × c^{z} 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 9000 = 2^{3} × 3^{2} × 5^{3}
Therefore, the total number of factors are (3 + 1) × (2 + 1) × (3 + 1) = 4 × 3 × 4 = 48 
Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 9000 and 843.
Solution:
The factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000 and factors of 843 are 1, 3, 281, 843.
Therefore, the Lowest Common Multiple (LCM) of 9000 and 843 is 2529000 and Highest Common Factor (HCF) of 9000 and 843 is 3. 
Example 3: Find if 3, 10, 45, 60, 100, 125, 1125 and 5375 are factors of 9000.
Solution:
When we divide 9000 by 5375 it leaves a remainder. Therefore, the number 5375 is not a factor of 9000. All numbers except 5375 are factors of 9000.

Example 4: Find the product of all the prime factors of 9000.
Solution:
Since, the prime factors of 9000 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 9000
What are the Factors of 9000?
The factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000 and its negative factors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.
What is the Sum of Factors of 9000?
Sum of all factors of 9000 = (2^{3 + 1}  1)/(2  1) × (3^{2 + 1}  1)/(3  1) × (5^{3 + 1}  1)/(5  1) = 30420
What Numbers are the Prime Factors of 9000?
The prime factors of 9000 are 2, 3, 5.
What is the Greatest Common Factor of 9000 and 3188?
The factors of 9000 and 3188 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000 and 1, 2, 4, 797, 1594, 3188 respectively.
Common factors of 9000 and 3188 are [1, 2, 4].
Hence, the Greatest Common Factor (GCF) of 9000 and 3188 is 4.
What are the Common Factors of 9000 and 2183?
Since, the factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000 and factors of 2183 are 1, 37, 59, 2183. Hence, 9000 and 2183 have only one common factor which is 1. Therefore, 9000 and 2183 are coprime.
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