What Are the Factors of 23?

The concept of factors of 23 plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Knowing factors helps in topics like divisibility, LCM and HCF, as well as logical reasoning found in school and competitive exams.

What Are Factors of 23?

A factor of 23 is a number that divides 23 exactly without leaving any remainder. In other words, when you divide 23 by its factor, the answer is a whole number. Since 23 is a prime number, the only factors of 23 are 1 and 23 itself. You’ll find this concept applied in finding LCM, HCF, prime factorization, and divisibility tests.

List of Factors of 23

The factors of 23 are:

Positive Factors	Negative Factors
1, 23	-1, -23

So, both 1 and 23 can divide 23 completely, and their negatives are also considered factors in higher mathematics.

Key Properties of Factors of 23

• 1 is a factor of every number.
• 23 is the largest factor of 23.
• 23 is a prime number, so it has only two factors.
• No other whole number divides 23 exactly.

How to Find Factors of 23

Follow these simple steps to find the factors of 23:

1. Start by checking if 1 divides 23. It does, since 23 ÷ 1 = 23 with no remainder.

2. Next, check the numbers from 2 up to 22. None of these numbers divides 23 evenly (23 is not divisible by 2, 3, ..., 22).

3. Finally, check if 23 divides itself. 23 ÷ 23 = 1 with no remainder.

4. Therefore, the only factors are 1 and 23.

You can use this technique for any number. Since 23 can only be divided by 1 and itself, it is confirmed as prime.

Prime Factorization of 23

The prime factorization of 23 shows the number as a product of prime numbers. As 23 has no other prime divisors:

23 = 1 × 23

So, the only prime factor is 23.

Factor Pairs of 23

Factor pairs multiply together to get 23. Since 23 is prime, there’s only one positive pair and one negative pair:

Positive Pair	Negative Pair
(1, 23)	(-1, -23)

Comparison: Factors of 23 and Other Numbers

Number	Factors
23	1, 23
24	1, 2, 3, 4, 6, 8, 12, 24
36	1, 2, 3, 4, 6, 9, 12, 18, 36

You can see that composite numbers like 24 and 36 have more factors than 23.

Solved Example: Quick Factor Check

Question: Is 23 a composite number?

1. A composite number must have more than two factors.

2. 23 has only 1 and 23 as factors.

Answer: No, 23 is not composite; it is a prime number.

Question: List all factors of 23, including negatives.

1. Positive factors are 1 and 23.

2. Negative factors are -1 and -23.

Full list: 1, 23, -1, -23

Practice Questions on Factors of 23

• Is 23 an even number? Explain your answer.
• Name all prime numbers between 20 and 30.
• Find which numbers from this list are factors of 23: 2, 3, 23, 46.
• Write down the factor pairs of 24 and compare with 23.
• Using divisibility rules, how do you check if a number is a factor of 23?

Key Takeaways on Factors of 23

• 23 has only two positive factors: 1 and 23.
• 23 is a prime number, not composite.
• Prime factorization of 23 is just 23 itself.
• Negative factors are also possible: -1, -23.

Classroom Tip

To quickly remember prime numbers like 23, use the trick: If you find no smaller number (other than 1) that can divide it exactly, the number is prime! Vedantu’s teachers often use a table of small primes in classes to help spot them instantly.

Relation to Other Concepts

The idea of factors of 23 connects closely with factors of 24, prime factorization, and topics like LCM and HCF. Mastering this helps you solve more advanced questions in algebra, arithmetic, and number theory.

We explored factors of 23—from the basic definition, step-by-step approach, properties, solved examples, and connections to other maths areas. Keep practicing with Vedantu for more confidence in mathematics and exams!

Explore related topics: Prime Numbers | Prime Factorization | Factors of 24 | Factors of 36