Factors of 144
The factors of 144 are integers that divide 144 completely, leaving no remainder. These factors can be positive or negative and usually come in pairs like (1, 144) and (-1, -144). Finding factors helps you understand how numbers are built and related to each other. You can discover the factors of 144 by testing smaller numbers or using prime factorization methods. Learning this concept is useful for topics such as multiples, least common multiples (LCM), and prime numbers. Here, you’ll find all factors, factor pairs, and the prime factorization of 144 explained simply.
What are the Factors of 144?
Factors of 144 are the numbers that divide it perfectly, leaving no remainder. The positive factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144, and if we include negatives, we get -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72 and -144. Each factor fits into 144 an exact number of times. Understanding factors helps identify whether a number is simple like a prime, or made up of smaller parts like a composite. 144 is composite because it’s made from the multiplication of smaller whole numbers.
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144
Factor Pairs of 144
When two numbers multiply to give 144, they form a factor pair. 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 ones are (-1, -144), (-2, -72), (-3, -48), (-4, -36), (-6, -24), (-8, -18), (-9, -16), (-12, -12). Each pair demonstrates how 144 can be created by multiplying two integers. Learning about factor pairs is useful in arithmetic and algebra. It helps in understanding divisibility, simplifying problems, and working with greatest common factors and prime numbers. You can also explore how factor pairs relate to the greatest common factor and prime factorization for deeper understanding.
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
To understand 144 more deeply, we can decompose it into its prime factors. By dividing step by step, we find that 144 can be written as 2 × 2 × 2 × 2 × 3 × 3. Hence, the prime factorization of 144 is 2^4 × 3^2. Prime factorization is an important concept in arithmetic and algebra because it helps in computing the LCM, greatest common factor, and simplifying complex 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?
The most effective way to find factors of 144 is to divide it by numbers up to its square root. Each divisor provides a matching factor, forming a pair that multiplies back to 144. This method not only finds all factors efficiently but also helps you understand the relationships between numbers. It's a practical way to explore factorization and basic arithmetic properties.
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 quickly identifies all factor pairs, making it especially helpful 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.