Is 79 a Prime Number or Composite? Explained with Steps
The concept of factors of 79 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Understanding the factors of numbers like 79 prepares students for topics such as divisibility, number theory, HCF, and LCM.
Understanding Factors of 79
A factor of 79 is a number that divides 79 exactly, without leaving any remainder. In simple terms, if you can multiply two whole numbers together to get 79, both numbers are its factors. This concept is widely used in prime number recognition, greatest common divisor (GCD), and identifying co-prime numbers.
How to Find the Factors of 79
To determine all the factors of 79, follow these steps:
1. Start with the number 1. 79 ÷ 1 = 79, remainder 0, so 1 is a factor.
2. Check numbers from 2 up to 79:
3. The only other exact division is 79 ÷ 79 = 1 (Remainder 0), so 79 is also a factor.
Therefore, the only factors of 79 are 1 and 79.
Is 79 a Prime Number?
Yes, 79 is a prime number because it has exactly two distinct positive factors: 1 and 79 itself. It is not divisible by any other number. This directly answers whether 79 is prime or composite – it is prime.
Pair Factors of 79
Pair factors are two numbers that multiply to give 79. The pair factors of 79 are:
(1, 79) and (79, 1).
If we consider negative numbers, the negative pair factors are: (-1, -79) and (-79, -1), because multiplying two negatives gives a positive.
Prime Factorization of 79
Since 79 is a prime number, its only prime factor is 79 itself. The prime factorization can be written as:
79 = 79 × 1
There are no other prime numbers that multiply to make 79.
Here’s a helpful table to understand factors of 79 more clearly:
Factors of 78, 79, and 80 Table
| Number | Factors | Prime/Composite? |
|---|---|---|
| 78 | 1, 2, 3, 6, 13, 26, 39, 78 | Composite |
| 79 | 1, 79 | Prime |
| 80 | 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 | Composite |
This table shows that 79 has only two factors, while neighboring numbers have several.
Worked Example – Stepwise Factor Check for 79
1. List all numbers from 1 to 79.
2. Divide 79 by each number:
3. Thus, the only factors of 79 are 1 and 79.
Practice Problems
- List all the factors of 79.
- Is 79 a co-prime with 80?
- What is the sum of all the factors of 79?
- Compare factors of 78, 79, and 80. Which is prime?
Common Mistakes to Avoid
- Thinking 79 has factors other than 1 and 79 because of its size.
- Confusing factors with multiples – multiples of 79 are numbers like 79, 158, etc.
- Forgetting that negative pairs also multiply to 79.
Real-World Applications
Understanding prime numbers such as 79 is important in cryptography, coding, number theory, and LCM/HCF calculations. Vedantu helps students see how factors and prime numbers have uses in secure communication, puzzles, and deeper maths studies.
We explored the idea of factors of 79, learned factorization steps, the difference between factors and multiples, how to check if a number is prime, and saw its importance in maths. Practice more with Vedantu to build confidence and strengthen your understanding of prime numbers and their properties.
To go further, read about Prime Numbers, how to find factors of a number, and the difference between factors and multiples. You may also compare with factors of 78 and factors of 81 to explore more prime and composite numbers.
FAQs on What Are the Factors of 79?
1. What are the factors of 79?
The factors of 79 are the numbers that divide it exactly without leaving a remainder. Since 79 is a prime number, it has only two factors: 1 and 79.
2. Is 79 a prime number?
Yes, 79 is a prime number because it has exactly two factors, which are 1 and 79 itself. It cannot be divided evenly by any other number.
3. How to find the factors of 79 step by step?
To find the factors of 79, follow these steps:
1. Start by dividing 79 by numbers starting from 1 upwards.
2. Check if the division leaves zero remainder.
3. Since 79 is only divisible by 1 and 79 itself, these are its only factors.
This confirms 79 is prime.
4. Is 79 a co-prime with 78 or other numbers?
Yes, 79 is co-prime with many numbers such as 78 because their only common factor is 1. Since 79 is prime and 78 is a composite number, they do not share other common factors.
5. What is the difference between factors and multiples of 79?
The factors of 79 are numbers that divide 79 exactly (remainder zero), which are 1 and 79. The multiples of 79 are obtained by multiplying 79 by any integer, such as 79, 158, 237, and so on.
6. What are the nearest numbers with more than two factors?
The numbers closest to 79 with more than two factors are 78 and 80. Both are composite numbers and have multiple factors, unlike 79, which is prime.
7. Why does 79 only have two factors?
79 has only two factors because it is a prime number. By definition, prime numbers have exactly two factors: 1 and the number itself. No other number divides 79 evenly.
8. Why do students sometimes confuse multiples and factors?
Students often confuse factors and multiples because both involve multiplication and division related to a number. Factors divide a number exactly, while multiples are products of the number with integers. Clear definitions and examples help avoid this confusion.
9. Can factors of 79 ever be negative?
Yes, factors of 79 can be negative as well, because multiplication of two negative numbers yields a positive product. Therefore, negative pairs like -1 and -79 are also factors of 79 in the broader mathematical sense, although generally only positive factors are listed.
10. How are factors of 79 useful for LCM/HCF questions?
Knowing the factors of 79 helps in solving LCM and HCF problems because:
• Factors help identify common divisors.
• Since 79 is prime, it often results in the HCF being 1 when paired with numbers not divisible by 79.
• It simplifies calculations involving multiples and divisors.
11. Do factors of 79 affect divisibility rules in exams?
While 79 itself is prime and does not contribute specific divisibility rules like small primes (2, 3, 5), understanding that 79 is only divisible by 1 and 79 helps students avoid mistakes and correctly identify divisibility and factors during exams.
12. Why is 79 co-prime with 78?
79 and 78 are co-prime because their only common factor is 1. Since 79 is prime and does not divide 78, this means they share no other factors, making their greatest common divisor equal to 1.
