Factors of 21
The factors of 21 are whole numbers that divide it exactly without leaving a remainder. They appear in positive and negative pairs, like (1, 21) or (-1, -21), 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 21, including all positive factors, factor pairs, and the prime factorization of 21 with step-by-step explanations and examples.
What are the Factors of 21?
There are 4 factors of 21. The factors of 21 are 1, 3, 7 and 21. Factors can be negative. The negative factors are -1, -3, -7 and -21. All of these numbers divides 21 completely. 21 is a composite number because it has other factors besides 1 and 21.
Factors of 21: 1, 3, 7 and 21
Factor Pairs of 21
The factor pairs of 21 are the pairs of integers that multiply together to give 21. These include both positive and negative combinations. The positive factor pairs of 21 are (1, 21), (3, 7), and the negative factor pairs are (-1, -21), (-3, -7). Knowing the factor pairs of 21 is useful for learning multiplication, division, and understanding concepts such as the greatest common factor and prime factorization.
Positive Factor Pairs of 21:
| Factor 1 | Factor 2 |
|---|---|
| 1 | 21 |
| 3 | 7 |
Negative Factor Pairs of 21:
| Factor 1 | Factor 2 |
|---|---|
| -1 | -21 |
| -3 | -7 |
Prime Factorization of 21
The prime factorization of 21 involves breaking it down into the product of prime numbers. Using division, we find that the prime factors of 21 are 3, 7. Therefore, the prime factorization of 21 is 3 × 7. Understanding prime factorization helps in finding GCF, LCM, and simplifying fractions.
Prime factors of 21:
3, 7
Prime factorization of 21:
3 × 7
Compact form:
3 × 7
Find prime factorization of any number with our Prime Factorization Calculator tool.
How to Find the Factors of 21?
To find the factors of 21 using the division method efficiently, you only need to check numbers up to the square root of 21. For every number that divides 21 evenly, both it and its corresponding pair (21 ÷ that number) are factors.
Optimized steps to find factors of 21:
- •21 ÷ 1 = 21 → ✅ Factor Pair: (1, 21)
- •21 ÷ 3 = 7 → ✅ Factor Pair: (3, 7)
This method avoids unnecessary checks and gives all factor pairs quickly. It's especially useful for larger numbers.
Find factors and factors pair of any number with our Factor Checker tool.
Frequently Asked Questions about factors of 21
What are the factors of 21?
The factors of 21 are 1, 3, 7, 21.
What is the prime factorization of 21?
The prime factorization of 21 is 3 × 7.
How do I find the factors of 21?
To find the factors of 21, start by dividing 21 by every number from 1 up to the square root of 21.
What are factor pairs of 21?
The factor pairs of 21 are (1, 21), (-1, -21), (3, 7), (-3, -7).
How can I use the factors of 21?
The factors of 21 can be used to simplify fractions, find the greatest common divisor (GCD), and determine multiples.
Are the factors of 21 always positive?
Factors can be both positive and negative. For example, the negative factors of 21 are -1, -3, -7, -21.