Factors of 4500
Factors of 4500 are integers that can be divided evenly into 4500. There are total 36 factors of 4500, of which 2, 3, 5 are its prime factors. The Prime Factorization of 4500 is 22 × 32 × 53.
- All Factors of 4500: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250 and 4500
- Prime Factors of 4500: 2, 3, 5
- Prime Factorization of 4500: 22 × 32 × 53
- Sum of Factors of 4500: 14196
1. | What Are the Factors of 4500? |
2. | Factors of 4500 by Prime Factorization |
3. | Factors of 4500 in Pairs |
4. | FAQs on Factors of 4500 |
What are Factors of 4500?
Factors of 4500 are pairs of those numbers whose products result in 4500. These factors are either prime numbers or composite numbers.
How to Find the Factors of 4500?
To find the factors of 4500, we will have to find the list of numbers that would divide 4500 without leaving any remainder.
- 4500/1500 = 3; therefore, 1500 is a factor of 4500 and 3 is also a factor of 4500.
- 4500/225 = 20; therefore, 225 is a factor of 4500 and 20 is also a factor of 4500.
☛ Also Check:
- Factors of 22 - The factors of 22 are 1, 2, 11, 22
- Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Factors of 121 - The factors of 121 are 1, 11, 121
- Factors of 125 - The factors of 125 are 1, 5, 25, 125
- Factors of 25 - The factors of 25 are 1, 5, 25
Factors of 4500 by Prime Factorization
- 4500 ÷ 2 = 2250
- 2250 ÷ 2 = 1125
Further dividing 1125 by 2 gives a non-zero 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 4500 can be written as 22 × 32 × 53 where 2, 3, 5 are prime.
Factors of 4500 in Pairs
Pair factors of 4500 are the pairs of numbers that when multiplied give the product 4500. The factors of 4500 in pairs are:
- 1 × 4500 = (1, 4500)
- 2 × 2250 = (2, 2250)
- 3 × 1500 = (3, 1500)
- 4 × 1125 = (4, 1125)
- 5 × 900 = (5, 900)
- 6 × 750 = (6, 750)
- 9 × 500 = (9, 500)
- 10 × 450 = (10, 450)
- 12 × 375 = (12, 375)
- 15 × 300 = (15, 300)
- 18 × 250 = (18, 250)
- 20 × 225 = (20, 225)
- 25 × 180 = (25, 180)
- 30 × 150 = (30, 150)
- 36 × 125 = (36, 125)
- 45 × 100 = (45, 100)
- 50 × 90 = (50, 90)
- 60 × 75 = (60, 75)
Negative pair factors of 4500 are:
- -1 × -4500 = (-1, -4500)
- -2 × -2250 = (-2, -2250)
- -3 × -1500 = (-3, -1500)
- -4 × -1125 = (-4, -1125)
- -5 × -900 = (-5, -900)
- -6 × -750 = (-6, -750)
- -9 × -500 = (-9, -500)
- -10 × -450 = (-10, -450)
- -12 × -375 = (-12, -375)
- -15 × -300 = (-15, -300)
- -18 × -250 = (-18, -250)
- -20 × -225 = (-20, -225)
- -25 × -180 = (-25, -180)
- -30 × -150 = (-30, -150)
- -36 × -125 = (-36, -125)
- -45 × -100 = (-45, -100)
- -50 × -90 = (-50, -90)
- -60 × -75 = (-60, -75)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 4500 Solved Examples
-
Example 1: How many factors are there for 4500?
Solution:
The factors of 4500 are too many, therefore if we can find the prime factorization of 4500, 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 4500 = 22 × 32 × 53
Therefore, the total number of factors are (2 + 1) × (2 + 1) × (3 + 1) = 3 × 3 × 4 = 36 -
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 4500 and 1756.
Solution:
The factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and factors of 1756 are 1, 2, 4, 439, 878, 1756.
Therefore, the Least Common Multiple (LCM) of 4500 and 1756 is 1975500 and Greatest Common Factor (GCF) of 4500 and 1756 is 4. -
Example 3: Find if 9, 90, 125, 180, 375, 750, 1125 and 3571 are factors of 4500.
Solution:
When we divide 4500 by 3571 it leaves a remainder. Therefore, the number 3571 is not a factor of 4500. All numbers except 3571 are factors of 4500.
-
Example 4: Find the product of all the prime factors of 4500.
Solution:
Since, the prime factors of 4500 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 4500
What are the Factors of 4500?
The factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -125, -150, -180, -225, -250, -300, -375, -450, -500, -750, -900, -1125, -1500, -2250, -4500.
What is the Sum of all Factors of 4500?
Sum of all factors of 4500 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (53 + 1 - 1)/(5 - 1) = 14196
What are Pair Factors of 4500?
The pair factors of 4500 are (1, 4500), (2, 2250), (3, 1500), (4, 1125), (5, 900), (6, 750), (9, 500), (10, 450), (12, 375), (15, 300), (18, 250), (20, 225), (25, 180), (30, 150), (36, 125), (45, 100), (50, 90), (60, 75).
What is the Greatest Common Factor of 4500 and 2242?
The factors of 4500 and 2242 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and 1, 2, 19, 38, 59, 118, 1121, 2242 respectively.
Common factors of 4500 and 2242 are [1, 2].
Hence, the Greatest Common Factor (GCF) of 4500 and 2242 is 2.
How Many Factors of 4500 are also Factors of 4128?
Since, the factors of 4500 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 125, 150, 180, 225, 250, 300, 375, 450, 500, 750, 900, 1125, 1500, 2250, 4500 and the factors of 4128 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 43, 48, 86, 96, 129, 172, 258, 344, 516, 688, 1032, 1376, 2064, 4128.
Hence, [1, 2, 3, 4, 6, 12] are the common factors of 4500 and 4128.
visual curriculum