Factors of 900

The numbers that divide 900 evenly are known as factors of 900. A factor of 900 is a number that divides the number without remainder. The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900.

Negative factors of 900: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -25, -30, -36, -45, -50, -60, -75, -90, -100, -150, -180, -225, -300, -450, and -900.

Prime factors of 900: 2, 3, and 5.

Prime factorization of 900: 2² × 3² × 5².

The sum of factors of 900: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 25 + 30 + 36 + 45 + 50 + 60 + 75 + 90 + 100 + 150 + 180 + 225 + 300 + 450 + 900 = 2970

Factors can be found using different methods. Mentioned below are some commonly used methods:

1. Finding factors using multiplication
2. Finding factors using the division method
3. Prime factors and Prime factorization

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 900. Identifying the numbers which are multiplied to get the number 900 is the multiplication method.

Step 1: Multiply 900 by 1, 900 × 1 = 900.

Step 2: Check for other numbers that give 900 after multiplying

2 × 450 = 900

3 × 300 = 900

4 × 225 = 900

5 × 180 = 900

6 × 150 = 900

9 × 100 = 900

10 × 90 = 900

12 × 75 = 900

15 × 60 = 900

18 × 50 = 900

20 × 45 = 900

25 × 36 = 900

30 × 30 = 900

Therefore, the positive factor pairs of 900 are: (1, 900), (2, 450), (3, 300), (4, 225), (5, 180), (6, 150), (9, 100), (10, 90), (12, 75), (15, 60), (18, 50), (20, 45), (25, 36), and (30, 30). For every positive factor, there is a negative factor.

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as a whole numbers as factors. Factors can be calculated by following the simple division method:

Step 1: Divide 900 by 1, 900 ÷ 1 = 900.

Step 2: Continue dividing 900 by the numbers until the remainder becomes 0.

900 ÷ 1 = 900

900 ÷ 2 = 450

900 ÷ 3 = 300

900 ÷ 4 = 225

900 ÷ 5 = 180

900 ÷ 6 = 150

900 ÷ 9 = 100

900 ÷ 10 = 90

900 ÷ 12 = 75

900 ÷ 15 = 60

900 ÷ 18 = 50

900 ÷ 20 = 45

900 ÷ 25 = 36

900 ÷ 30 = 30

Therefore, the factors of 900 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, and 900.

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

• Using prime factorization
• Using factor tree

Using Prime Factorization: In this process, prime factors of 900 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

900 ÷ 2 = 450

450 ÷ 2 = 225

225 ÷ 3 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

The prime factors of 900 are 2, 3, and 5. The prime factorization of 900 is: 2² × 3² × 5².

The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:

Step 1: Firstly, 900 is divided by 2 to get 450.

Step 2: Now divide 450 by 2 to get 225.

Step 3: Then divide 225 by 3 to get 75.

Step 4: Divide 75 by 3 to get 25.

Step 5: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 900 is: 2² × 3² × 5².

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

• Positive factor pairs of 900: (1, 900), (2, 450), (3, 300), (4, 225), (5, 180), (6, 150), (9, 100), (10, 90), (12, 75), (15, 60), (18, 50), (20, 45), (25, 36), and (30, 30).
• Negative factor pairs of 900: (-1, -900), (-2, -450), (-3, -300), (-4, -225), (-5, -180), (-6, -150), (-9, -100), (-10, -90), (-12, -75), (-15, -60), (-18, -50), (-20, -45), (-25, -36), and (-30, -30).

• Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 900 are 1, 2, 3, 4, 5, etc.

• Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 900.

• Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 900 are (1, 900), (2, 450), etc.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 900 is 2² × 3² × 5².

• Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method to find factors of 900 involves identifying pairs like (1, 900), (2, 450), etc.