Factors of 84
The factors of 84 are integers that divide 84 completely, leaving no remainder. These factors can be positive or negative and usually come in pairs like (1, 84) and (-1, -84). Finding factors helps you understand how numbers are built and related to each other. You can discover the factors of 84 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 84 explained simply.
What are the Factors of 84?
Factors of 84 are the numbers that divide it perfectly, leaving no remainder. The positive factors are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84, and if we include negatives, we get -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42 and -84. Each factor fits into 84 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. 84 is composite because it’s made from the multiplication of smaller whole numbers.
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
Factor Pairs of 84
When two numbers multiply to give 84, they form a factor pair. The positive factor pairs of 84 are (1, 84), (2, 42), (3, 28), (4, 21), (6, 14), (7, 12), and the negative ones are (-1, -84), (-2, -42), (-3, -28), (-4, -21), (-6, -14), (-7, -12). Each pair demonstrates how 84 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 84:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 84 |
| 2 | 42 |
| 3 | 28 |
| 4 | 21 |
| 6 | 14 |
| 7 | 12 |
Negative Factor Pairs of 84:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -84 |
| -2 | -42 |
| -3 | -28 |
| -4 | -21 |
| -6 | -14 |
| -7 | -12 |
Prime Factorization of 84
To understand 84 more deeply, we can decompose it into its prime factors. By dividing step by step, we find that 84 can be written as 2 × 2 × 3 × 7. Hence, the prime factorization of 84 is 2^2 × 3 × 7. 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 84:
2, 2, 3, 7
Prime factorization of 84:
2 × 2 × 3 × 7
Compact form:
22 × 3 × 7
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 84?
The most effective way to find factors of 84 is to divide it by numbers up to its square root. Each divisor provides a matching factor, forming a pair that multiplies back to 84. 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 84:
- •84 ÷ 1 = 84 → ✅ Factor Pair: (1, 84)
- •84 ÷ 2 = 42 → ✅ Factor Pair: (2, 42)
- •84 ÷ 3 = 28 → ✅ Factor Pair: (3, 28)
- •84 ÷ 4 = 21 → ✅ Factor Pair: (4, 21)
- •84 ÷ 6 = 14 → ✅ Factor Pair: (6, 14)
- •84 ÷ 7 = 12 → ✅ Factor Pair: (7, 12)
This method avoids unnecessary checks and quickly identifies all factor pairs, making it especially helpful for larger numbers.
Find factors and factor pairs of any number with our Factor Checker tool.
Frequently Asked Questions about factors of 84
What are the factors of 84?
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
What is the prime factorization of 84?
The prime factorization of 84 is 2 × 2 × 3 × 7.
How do I find the factors of 84?
To find the factors of 84, start by dividing 84 by every number from 1 up to the square root of 84.
What are factor pairs of 84?
The factor pairs of 84 are (1, 84), (-1, -84), (2, 42), (-2, -42), (3, 28), (-3, -28), (4, 21), (-4, -21), (6, 14), (-6, -14), (7, 12), (-7, -12).
How can I use the factors of 84?
The factors of 84 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 84 always positive?
Factors can be both positive and negative. For example, the negative factors of 84 are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -84.