Factors of 900
The factors of 900 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 900) or (-1, -900), and are always integers, never fractions or decimals. You can find them using methods such as division or prime factorization. Learning about factors helps build a foundation for understanding divisibility, multiples, and prime numbers. In this guide, we'll explore the different types of factors of 900, including all positive factors, factor pairs, and the prime factorization of 900 with step-by-step explanations and examples.
What are the Factors of 900?
There are 27 factors of 900. 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. Factors can be negative. The negative factors 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. All of these numbers divides 900 completely. 900 is a composite number because it has other factors besides 1 and 900.
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
Factor Pairs of 900
The factor pairs of 900 are the pairs of integers that multiply together to give 900. These include both positive and negative combinations. 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), (30, 30), and the negative factor pairs 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), (-30, -30). Knowing the factor pairs of 900 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 900:
| Factor 1 | Factor 2 |
|---|---|
| 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 |
| 30 | 30 |
Negative Factor Pairs of 900:
| Factor 1 | Factor 2 |
|---|---|
| -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 |
| -30 | -30 |
Prime Factorization of 900
The prime factorization of 900 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 900 are 2, 2, 3, 3, 5, 5. Therefore, the prime factorization of 900 is 2^2 × 3^2 × 5^2. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 900:
2, 2, 3, 3, 5, 5
Prime factorization of 900:
2 × 2 × 3 × 3 × 5 × 5
Compact form:
22 × 32 × 52
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How to Find the Factors of 900?
To find the factors of 900 using the division method efficiently, you only need to check numbers up to the square root of 900. For every number that divides 900 evenly, both it and its corresponding pair (900 ÷ that number) are factors.
Optimized steps to find factors of 900:
- •900 ÷ 1 = 900 → ✅ Factor Pair: (1, 900)
- •900 ÷ 2 = 450 → ✅ Factor Pair: (2, 450)
- •900 ÷ 3 = 300 → ✅ Factor Pair: (3, 300)
- •900 ÷ 4 = 225 → ✅ Factor Pair: (4, 225)
- •900 ÷ 5 = 180 → ✅ Factor Pair: (5, 180)
- •900 ÷ 6 = 150 → ✅ Factor Pair: (6, 150)
- •900 ÷ 9 = 100 → ✅ Factor Pair: (9, 100)
- •900 ÷ 10 = 90 → ✅ Factor Pair: (10, 90)
- •900 ÷ 12 = 75 → ✅ Factor Pair: (12, 75)
- •900 ÷ 15 = 60 → ✅ Factor Pair: (15, 60)
- •900 ÷ 18 = 50 → ✅ Factor Pair: (18, 50)
- •900 ÷ 20 = 45 → ✅ Factor Pair: (20, 45)
- •900 ÷ 25 = 36 → ✅ Factor Pair: (25, 36)
- •900 ÷ 30 = 30 → ✅ Factor
This method avoids unnecessary checks and gives all factor pairs quickly. It's especially useful for larger numbers.
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Frequently Asked Questions about factors of 900
What are the factors of 900?
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, 900.
What is the prime factorization of 900?
The prime factorization of 900 is 2 × 2 × 3 × 3 × 5 × 5.
How do I find the factors of 900?
To find the factors of 900, start by dividing 900 by every number from 1 up to the square root of 900.
What are factor pairs of 900?
The factor pairs of 900 are (1, 900), (-1, -900), (2, 450), (-2, -450), (3, 300), (-3, -300), (4, 225), (-4, -225), (5, 180), (-5, -180), (6, 150), (-6, -150), (9, 100), (-9, -100), (10, 90), (-10, -90), (12, 75), (-12, -75), (15, 60), (-15, -60), (18, 50), (-18, -50), (20, 45), (-20, -45), (25, 36), (-25, -36), (30, 30), (-30, -30).
How can I use the factors of 900?
The factors of 900 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 900 always positive?
Factors can be both positive and negative. For example, the negative 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, -900.