Factors of 144
The factors of 144 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 144) or (-1, -144), 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 144, including all positive factors, factor pairs, and the prime factorization of 144 with step-by-step explanations and examples.
What are the Factors of 144?
There are 15 factors of 144. The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144. Factors can be negative. The negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72 and -144. All of these numbers divides 144 completely. 144 is a composite number because it has other factors besides 1 and 144.
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144
Factor Pairs of 144
The factor pairs of 144 are the pairs of integers that multiply together to give 144. These include both positive and negative combinations. The positive factor pairs of 144 are (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), (12, 12), and the negative factor pairs are (-1, -144), (-2, -72), (-3, -48), (-4, -36), (-6, -24), (-8, -18), (-9, -16), (-12, -12). Knowing the factor pairs of 144 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 144:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 144 |
| 2 | 72 |
| 3 | 48 |
| 4 | 36 |
| 6 | 24 |
| 8 | 18 |
| 9 | 16 |
| 12 | 12 |
Negative Factor Pairs of 144:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -144 |
| -2 | -72 |
| -3 | -48 |
| -4 | -36 |
| -6 | -24 |
| -8 | -18 |
| -9 | -16 |
| -12 | -12 |
Prime Factorization of 144
The prime factorization of 144 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 144 are 2, 2, 2, 2, 3, 3. Therefore, the prime factorization of 144 is 2^4 × 3^2. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 144:
2, 2, 2, 2, 3, 3
Prime factorization of 144:
2 × 2 × 2 × 2 × 3 × 3
Compact form:
24 × 32
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How to Find the Factors of 144?
To find the factors of 144 using the division method efficiently, you only need to check numbers up to the square root of 144. For every number that divides 144 evenly, both it and its corresponding pair (144 ÷ that number) are factors.
Optimized steps to find factors of 144:
- •144 ÷ 1 = 144 → ✅ Factor Pair: (1, 144)
- •144 ÷ 2 = 72 → ✅ Factor Pair: (2, 72)
- •144 ÷ 3 = 48 → ✅ Factor Pair: (3, 48)
- •144 ÷ 4 = 36 → ✅ Factor Pair: (4, 36)
- •144 ÷ 6 = 24 → ✅ Factor Pair: (6, 24)
- •144 ÷ 8 = 18 → ✅ Factor Pair: (8, 18)
- •144 ÷ 9 = 16 → ✅ Factor Pair: (9, 16)
- •144 ÷ 12 = 12 → ✅ 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 144
What are the factors of 144?
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
What is the prime factorization of 144?
The prime factorization of 144 is 2 × 2 × 2 × 2 × 3 × 3.
How do I find the factors of 144?
To find the factors of 144, start by dividing 144 by every number from 1 up to the square root of 144.
What are factor pairs of 144?
The factor pairs of 144 are (1, 144), (-1, -144), (2, 72), (-2, -72), (3, 48), (-3, -48), (4, 36), (-4, -36), (6, 24), (-6, -24), (8, 18), (-8, -18), (9, 16), (-9, -16), (12, 12), (-12, -12).
How can I use the factors of 144?
The factors of 144 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 144 always positive?
Factors can be both positive and negative. For example, the negative factors of 144 are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, -144.