Factors of 1500

Every number greater than 1 will have a minimum of 2 factors. 

Factors of 1500: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, and 1500.

Negative factors of 1500: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, and -1500.

Prime factorization of 1500: 2²×5³×3

Sum of factors of 1500: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 25 + 30 + 50 + 60 + 75 + 100 + 125 + 150 + 250 + 300 + 375 + 500 + 750 + 1500 = 4368.
 

The methods mentioned below can be used to find the factors of 1500. Use any factor-finding method that is easy for you. 

1. Multiplication method 
2. Division method 
3. Prime factorization and prime factors method
4. Factor tree method

Steps:

• Find the pair of numbers which when multiplied gives 1500.

• 1500 is a composite number because it has more than 2 factors.

• The factor pairs of 1500 are:

Positive factor pairs — (1,1500) (2,750) (3,500) (4,375) (5,300) (6,250) (10,150) (12,125) (15,100) (20,75) (25,60) (30,50)

Negative factor pairs — (-1,-1500) (-2,-750) (-3,-500) (-4,-375) (-5,-300) (-6,-250) (-10,-150) (-12,-125) (-15,-100) (-20,-75) (-25,-60) (-30,-50)

Steps: 

1. Start dividing 1500 with small numbers and check the remainder.
2. Dividend = Divisor x Quotient + Remainder
3. The factors of 1500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, 1500. Negative factors are -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, and -1500.

Prime factors of 1500: 2, 3, and 5. 

Prime factorization of 1500: 1500 = 2 × 2 × 3 × 5 × 5 × 5

Positive factors of 1500 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 125, 150, 250, 300, 375, 500, 750, and 1500. 

Negative factors are: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -125, -150, -250, -300, -375, -500, -750, and -1500.

Factor tree is a graphical representation of breaking down any number into prime factors.

In case of 1500, 

Step 1: First, we write the number on top (in this case, 1500). From there, it will be broken down into 2 parts.
Step 2: Fill in the factor pairs of 1500 in separate steps. In this step, the number will be factorized into 2 and 750.
Step 3: In this step, 750 will again be factorized into 375 and 2. Then it will be factorized down to 375 and 2. We will do the same for 375 and split it into 5 and 75.
Step 4: We will do the same for 75 and break it down into 5 and 15. We can split 15 also into its prime factors, they are 3 and 5.
Step 5: From this, we can find that the prime factors of 1500 are 2, 3, and 5. This is how the factor tree helps to visualize the factors easily to students.
 

Factor pairs are a combination of two numbers, a and b, whose product is equal to 1500. So, over here, a and b are a factor pair of 1500.

The factor pairs of 1500 are

Positive factor pairs:(1,1500), (2,750), (3,500), (4,375), (5,300), (6,250), (10,150), (12,125), (15,100), (20,75), (25,60), (30,50)

Negative factor pairs : (-1,-1500), (-2,-750), (-3,-500), (-4,-375), (-5,-300), (-6,-250), (-10,-150), (-12,-125), (-15,-100), (-20,-75), (-25,-60), (-30,-50)

• Factors: The numbers which multiplied with each other to get the required numbers are called factors of that number. Example: Factors of 12 are:1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12. Here, 1, 2, 6, 3, 4 and 12 are the factors of 12.

• Greatest Common Factor (GCF): The greatest number that divides the given number exactly and is a common factor for the given number is called GCF. An example for GCF is: The GCF of 1500, 10, and 100 is 10. Because it is the greatest factor that is common for all three numbers.

• Prime number: Any number greater than 1 and has only 2 factors is called a prime number. Example: 811/1 = 811 and 811/811 = 1. We can see that 811 can be divided exactly by only 2 numbers. Those two numbers are 1 and 811.

• Divisor: Any number that divides another number exactly and leaves no remainder is called a divisor. When we divide 12 by 3, we get a quotient of 4. Here, the divisor is 3 and the dividend is 12.