How to Find Factors of 59 Step by Step
The concept of factors of 59 is essential in mathematics and helps in solving real-world and exam-level problems efficiently.
Understanding Factors of 59
A factor of 59 is a whole number that divides 59 exactly, leaving no remainder. In mathematics, factors help us check divisibility, solve equations, and quickly understand whether a number is prime or composite. This concept is widely used in divisors of numbers, prime factorization, and checking multiples.
What Are the Factors of 59?
The factors of 59 are the numbers that can divide 59 without leaving any remainder. Because 59 is a prime number, its only factors are 1 and 59. So, 59 does not have any other positive divisors except 1 and itself. Negative factors are -1 and -59, but usually factors refer to positive numbers unless negatives are specifically needed.
Step-by-Step: How to Find Factors of 59
To find all factors of 59, follow these steps:
1. Start by checking if 1 divides 59 exactly: 59 ÷ 1 = 59 (remainder 0) — so 1 is a factor.
2. Check numbers greater than 1 and less than 59 (2, 3, 4, ..., 58). None of these divide 59 without a remainder.
3. Finally, check 59 ÷ 59 = 1 (remainder 0) — so 59 is a factor.
Therefore, the factors of 59 are 1 and 59.
Is 59 Prime or Composite?
A prime number has exactly two distinct positive factors: 1 and itself. A composite number has more than two. Since 59 is only divisible by 1 and 59, it is a prime number. This is important for recognizing prime factorization patterns and for upcoming board exams.
Pair Factors of 59
Pair factors are pairs of numbers which, when multiplied, give 59. For 59:
- Positive pair factors: (1, 59)
- Negative pair factors: (-1, -59)
Table of Factors of 59
Here’s a helpful table to understand factors of 59 more clearly:
Factors of 59 Table
| Divisor | Result | Remainder | Is Factor? |
|---|---|---|---|
| 1 | 59 ÷ 1 = 59 | 0 | Yes |
| 2 | 59 ÷ 2 = 29.5 | 1 | No |
| 59 | 59 ÷ 59 = 1 | 0 | Yes |
This table shows that only 1 and 59 divide 59 exactly. No other whole number divides 59 without a remainder.
Prime Factorization of 59
Prime factorization is expressing 59 as a product of prime numbers.
- Since 59 is already a prime, its prime factorization is simply 59.
- You can write it as 1 × 59 or just 59.
- There are no other prime factors.
Worked Example – Solving a Problem
Let’s find if 7 is a factor of 59:
1. Divide 59 by 7: 59 ÷ 7 = 8.428...2. The result is not a whole number.
3. Check the remainder: 7 × 8 = 56, 59 - 56 = 3 (remainder is not zero).
Therefore, 7 is not a factor of 59.
Difference Between Factors and Multiples (with Example)
- Factors of a number are numbers that divide it exactly (e.g., 1 and 59 for 59).
- Multiples of a number are what you get when you multiply it by whole numbers (e.g., 59, 118, 177, ... for 59).
Understanding this difference helps avoid confusion in exams and makes problem solving faster.
Factors of Numbers Near 59
It’s good to explore factors of nearby numbers to see patterns and test your skills:
- Factors of 58 (composite: 1, 2, 29, 58)
- Factors of 60 (composite: 1, 2, 3, 4, 5, 6, ...)
- Factors of 61 (prime: 1, 61)
Check more about Prime Numbers to learn more about why 59 is a prime!
Practice Problems
- List all the factors of 59.
- Is 13 a factor of 59?
- Find the common factors of 59 and 58.
- Is 59 a multiple of 7?
- Give another example of a 2-digit prime number and its factors.
Common Mistakes to Avoid
- Listing numbers like 3, 5, or 7 as factors of 59.
- Believing that all odd numbers are prime (not true for numbers like 9, 15, etc.).
- Confusing factors (divisors) with multiples.
How Factors of 59 Help in Exams and Real Life
Knowing the factors of 59 helps you solve LCM, HCF, and divisibility problems in maths and competitive exams. It also improves quick calculations for mental maths, coding, and grouping items. Vedantu helps students build a strong foundation in such concepts, so you can easily handle similar questions in any class or exam scenario.
We explored the idea of factors of 59, checked if it is prime, learned easy ways to find and use factors, and practiced with examples. Practice more with Vedantu to gain confidence and excel in your exams!
For more on this concept, visit Factors of a Number and strengthen your maths basics, including Divisibility Rules, Prime Factors, and how to find Multiples for other numbers. Explore topics like Even and Odd Numbers and LCM and HCF for a complete understanding.
FAQs on What Are the Factors of 59?
1. What are the factors of 59?
The factors of 59 are the numbers that divide 59 exactly without leaving a remainder. Since 59 is a prime number, its only factors are 1 and 59.
2. Is 59 a prime or composite number?
The number 59 is a prime number. It has exactly two factors: 1 and 59 itself, with no other divisors.
3. How to find if a number divides 59?
To check if a number divides 59, divide 59 by that number. If the remainder is zero, then it is a factor of 59. Since 59 is prime, only division by 1 and 59 results in zero remainder.
4. What are the multiples of 59?
The multiples of 59 are numbers obtained by multiplying 59 by integers like 1, 2, 3, etc. For example, 59, 118, 177, 236, etc., are multiples of 59. Multiples are different from factors, which divide the number.
5. Is 7 a factor of 59?
No, 7 is not a factor of 59 because 59 divided by 7 leaves a remainder. Only numbers that divide 59 exactly without remainder, which are 1 and 59, are factors.
6. Why is 59 not a multiple of 7?
59 is not a multiple of 7 because multiples of 7 are obtained by multiplying 7 by whole numbers, such as 7, 14, 21, and so on. Since 59 does not appear in this list, it cannot be a multiple of 7.
7. Why do students confuse prime factors with all factors?
Students often confuse prime factors with all factors because both relate to divisibility. However, factors include all numbers that divide the number, while prime factors are only the prime numbers among those factors. Understanding this distinction is essential for factorization and problem-solving.
8. Should 0 be included as a factor?
No, 0 is not considered a factor of any number because division by zero is undefined. Factors are numbers that divide the given number without a remainder, which excludes zero.
9. Why do factors matter for LCM and HCF?
Factors are fundamental in calculating the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of numbers. The HCF is found by identifying common factors of numbers, while the LCM is based on common multiples. Knowing factors helps solve problems involving divisibility, fractions, and algebra.
10. How are factors relevant in quadratic equations?
Factors help in solving and simplifying quadratic equations by expressing them as products of binomials. Factorization allows finding the roots of quadratic equations easily, making it a key concept for students learning algebra.
