Is 43 a Prime Number or Composite—How Do You Find Its Factors?
The concept of factors of 43 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Knowing how to find factors of a number lays the foundation for understanding divisibility, multiplication, prime numbers, and more. Here, you will find a clear explanation, step-by-step method to find all factors of 43, along with worked examples and handy comparison tables to make learning easier with Vedantu.
Understanding Factors of 43
A factor of 43 is a whole number that divides 43 exactly, leaving no remainder. In other words, if you multiply two whole numbers to get 43, then each of those numbers is a factor of 43. This concept is widely used in finding prime numbers, exploring divisibility rules, and learning about factor pairs. Understanding the factors of 43 helps students identify whether a number is prime or composite and lays the groundwork for more advanced topics like prime factorization and multiples.
How to Find Factors of 43?
To find the factors of 43, follow these steps:
1. Start with 1. Every whole number is divisible by 1.
2. Divide 43 by 2. The result is 21.5, which is not a whole number, so 2 is not a factor.
3. Test all integers between 2 and 42, by dividing 43 by each number: None will give a whole number quotient, except for 43 itself.
4. 43 divided by 43 equals 1 exactly, so 43 is a factor.
Therefore, the only factors of 43 are 1 and 43.
Is 43 a Prime Number?
Yes, 43 is a prime number because it has exactly two distinct positive factors: 1 and itself (43). No other whole number divides 43 evenly.
Complete List and Pair Factors of 43
Here’s a handy table of the factors and pairs for quick revision:
Factors of 43 Table
| Factor | Multiplication Pair | Explained |
|---|---|---|
| 1 | 1 × 43 = 43 | Positive factor, divides evenly |
| 43 | 43 × 1 = 43 | Positive factor, divides evenly |
| -1 | -1 × -43 = 43 | Negative factor |
| -43 | -43 × -1 = 43 | Negative factor |
This table shows that 1 and 43 (and their negatives) are the only factors of 43, confirming that 43 is prime.
Prime Factorisation of 43
The prime factorisation of 43 is simple—since 43 is prime, its only prime factor is 43 itself. 43 = 43 × 1. In other words, there are no smaller prime numbers that multiply to give 43 (other than 1 × 43).
Pair Factors Explained
Pair factors are sets of two whole numbers which multiply to 43. For 43, the pair factors are (1, 43) and (43, 1). If you include negative integers, negative pairs are (-1, -43) and (-43, -1). These pairs help reinforce the idea that there are no other possible integer combinations to make 43.
Worked Example – Solving a Problem
Let’s solve an example to find all the factors of 43:
Step 1. Divide 43 by 1: 43 ÷ 1 = 43. Remainder is 0.
Step 2. Test 43 ÷ 2 = 21.5. Not an integer, so 2 is not a factor.
Step 3. Try dividing by numbers up to 42 (3, 4, 5 … 42): None of these results in a whole number.
Step 4. Divide 43 by 43: 43 ÷ 43 = 1. Remainder is 0.
Step 5. List out all numbers with remainder 0 when divided into 43 — only 1 and 43.
Final Answer: The factors of 43 are 1 and 43.
Common Mistakes to Avoid
- Assuming 43 is composite and trying to break it into more factors
- Confusing factors with multiples—remember, factors divide the number, multiples are products of the number
- Forgetting that every prime number has only two factors: 1 and itself
Factors vs Multiples – Quick Comparison
| Term | Definition | Example with 43 |
|---|---|---|
| Factor | Number that divides 43 completely | 1, 43 |
| Multiple | Number you get when multiplying 43 by any integer | 43, 86, 129, 172... |
This mini-table helps students quickly see how factors and multiples differ for the number 43.
Practice Problems
- Is 43 a composite number?
- List the pair factors of 43.
- Find the sum of all factors of 43.
- What is the GCF of 43 and 129?
- Are there any common factors between 43 and 53?
Related Numbers and Further Learning
Want to compare factors of numbers close to 43? Check out these Vedantu resources:
Factors of 42 |
Factors of 44 |
Factors of 41 |
Factors of 45 |
Factors of 47
Explore also: Prime Numbers | How to Find Factors of a Number | Table of 43 | What are Factors? | Factors of 51
Summary
We explored the idea of factors of 43, how to identify them, confirm that 43 is a prime number, and compare its factors with other nearby numbers. Practice more with Vedantu to build confidence in maths concepts like divisibility, primes, and factorization. For further support and easy-to-understand explanations, check out more resources on Vedantu’s maths pages!
FAQs on What Are the Factors of 43?
1. What are the factors for 43?
The factors of 43 are 1 and 43 because these are the only numbers that divide 43 exactly without leaving any remainder. Since 43 is a prime number, it has no other factors.
2. Is 43 a prime number?
Yes, 43 is a prime number as it has exactly two distinct factors: 1 and 43. It cannot be divided evenly by any other whole number.
3. How to factorise 43?
To factorise 43, check for divisibility by numbers from 1 to the square root of 43. Since none of these numbers except 1 divides 43 exactly, the prime factorisation of 43 is simply 43 itself.
4. Is 43 a factor of zero?
Yes, 43 is a factor of zero because any non-zero number divides zero evenly. So, zero can be divided by 43 to give zero remainder, but zero is not considered a factor of 43.
5. What is the prime factor of 43?
Since 43 is a prime number, its only prime factor is 43 itself.
6. What is the sum of all factors of 43?
The factors of 43 are 1 and 43. Adding these gives the sum: 1 + 43 = 44. So, the sum of all factors of 43 is 44.
7. What are the common factors of 43 and 53?
The factors of 43 are 1 and 43. The factors of 53 are 1 and 53. Therefore, the only common factor of 43 and 53 is 1.
8. What is the greatest common factor of 43 and 129?
The factors of 43 are 1 and 43. The factors of 129 are 1, 3, 43, and 129. Hence, the greatest common factor (GCF) of 43 and 129 is 43.
9. Why is 43 not a multiple of any number except 1 and 43?
Because 43 is a prime number, it does not have multiples other than the products of 1 and itself with other numbers. Its only factors are 1 and 43, so it cannot be evenly divided by any other number, making it unique in multiplication tables.
10. How does knowing if 43 is prime help in avoiding exam calculation mistakes?
Knowing that 43 is a prime number helps students avoid trying to divide it by irrelevant numbers during factorisation or simplification problems. This improves accuracy and speeds up problem solving in exams by focusing only on relevant factors.
11. Can 43 be a factor in any multiplication table except its own?
No, 43 cannot be a factor in multiplication tables other than its own because it has no factors other than 1 and itself. It appears only in the multiplication table of 43, confirming its status as a prime number.
12. Why do many factor tables exclude prime numbers other than listing 1 and itself?
Prime numbers like 43 have only two factors, 1 and themselves. Since this is simple and does not offer multiple factor pairs, many factor tables mention just these two to keep the list concise and focus on composite numbers with multiple factors.
