How to Find the Factors and Pair of 19 in Maths?
The concept of factors of 19 is essential in mathematics and helps students understand divisibility, prime numbers, and aids in quick problem-solving, especially in exams and real-life maths situations.
Understanding Factors of 19
A factor of 19 is a whole number that divides 19 exactly, leaving no remainder. Since 19 is a prime number, it has only two distinct factors: 1 and 19. This property is important in number theory, arithmetic, and when learning about prime numbers, factors of a number, and divisibility rules.
Definition and Key Points
Factors of a number are the integers that divide the number completely (with remainder zero). For 19:
- 1 × 19 = 19; these are called “factor pairs”.
- 19 is a prime number, so it has exactly two positive factors—1 and itself.
How to Find the Factors of 19 – Step by Step
Let’s check all possible divisors of 19 to find its factors. Always start with 1 and the number itself for any positive integer:
2. Divide 19 by 2.
3. Divide 19 by all numbers up to 19:
- 19 ÷ 19 = 1 (remainder 0) ⇒ 19 is a factor.
So, the only positive factors of 19 are 1 and 19.
Factors of 19 in Words
For exams or oral tests, you might need to write the factors of 19 in words: “one and nineteen”. This means the factors of 19 are one and nineteen.
Pair Factors of 19
Factors can also be written as pairs for easy understanding. A factor pair is two numbers multiplied together to give the original number. For 19:
- Negative factor pair: (-1, -19) (because (-1) × (-19) = 19)
Here’s a helpful table to see factor pairs of 19:
Factor Pairs of 19
| Factor 1 | Factor 2 | Product |
|---|---|---|
| 1 | 19 | 19 |
| -1 | -19 | 19 |
This shows that only these pairs multiply to 19 without remainder.
Prime Factorisation of 19
Prime factorisation is writing a number as a product of its prime factors. Since 19 itself is prime, its only prime factor is 19.
No further breakdown is possible. 19 is its own prime factor.
Difference Between Factors and Multiples
Factors of 19 are numbers that divide 19 exactly. Multiples of 19 are numbers you get when you multiply 19 by 1, 2, 3, etc.
Examples:
- 20 is not a factor of 19.
- First 3 multiples of 19: 19, 38, 57.
Related Numbers – Factors of 18, 20, and More
Comparing factors of 19 with neighbouring numbers helps build a stronger understanding.
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 21: 1, 3, 7, 21
- Factors of 12: 1, 2, 3, 4, 6, 12
Worked Example – Step-by-Step Solution
Let’s find all the factors of 19 using division:
2. Divide 19 by 2: 19 ÷ 2 = 9.5 (Not a whole number. 2 is NOT a factor.)
3. Try dividing 19 by each number up to 19. Only 1 and 19 give whole numbers.
4. So, the factors are 1 and 19.
Practice Problems
2. What are the factors of 19 in words?
3. Is 7 a factor of 19?
4. What are the multiples of 19 up to 100?
Quick Revision Table
| Number | All Factors | Prime/Composite? |
|---|---|---|
| 19 | 1, 19 | Prime |
We explored the idea of factors of 19, how to find them step-by-step, used prime factorisation, and compared with related numbers. For more maths help, solutions and practice, visit Vedantu’s maths section.
- Prime Numbers
- Factors of a Number
- Factors of 18
- Factors of 20
- Factors of 21
- Factors of 12
FAQs on What Are the Factors of 19?
1. What are the factors of 19?
The **factors of 19** are the numbers that divide 19 exactly without leaving a remainder. Since 19 is a **prime number**, it has only two factors: 1 and 19. These are the only positive integers that multiply to give 19.
2. Is 19 a prime number?
Yes, 19 is a prime number because it has exactly two factors: 1 and itself (19). A prime number is a number greater than 1 that cannot be divided evenly by any other numbers.
3. What are the multiples of 19?
The multiples of 19 are numbers obtained by multiplying 19 with whole numbers. They are different from factors because multiples are the results of multiplication, whereas factors divide the number exactly. For example, the first few multiples of 19 are 19, 38, 57, 76, and 95.
4. Is 7 a factor of 19?
No, 7 is not a factor of 19. When 19 is divided by 7, it leaves a remainder, which means 7 does not divide 19 exactly. Therefore, 7 cannot be a factor of 19.
5. How do you write the factors of 19 in words?
The factors of 19 written in words are one and nineteen. This format is important for written and oral exam answers, where clarity in number names is required.
6. How many factors does 19 have?
Number 19 has exactly two factors: 1 and 19. This is because 19 is a prime number, and all prime numbers have only two factors—1 and themselves.
7. Why is 19 not divisible by numbers other than 1 and 19?
19 is not divisible by any other numbers except 1 and 19 because it is a prime number. Prime numbers cannot be evenly divided (without remainder) by numbers other than these two, as they have no smaller divisors.
8. Why do students confuse factors with multiples for 19?
Students often confuse factors and multiples because both relate to division and multiplication. However, factors of 19 divide it exactly with zero remainder, while multiples of 19 are products of 19 with other whole numbers. Clear understanding helps reduce common exam mistakes.
9. Why is understanding factors of prime numbers important for exams?
Understanding the factors of prime numbers like 19 is important because it helps in factorization, simplifying fractions, and solving algebraic problems. Many exam questions test knowledge of prime factors and their unique properties.
10. Can 19 have negative factors?
Yes, 19 has corresponding negative factors which are the negative versions of its positive factors. So, the negative factors of 19 are -1 and -19, since multiplying two negative numbers also results in a positive product.
11. Why do some write factors in pairs, and what does that mean?
Writing factors in pairs means identifying two numbers that multiply together to give the original number. For 19, since it is prime, the only factor pairs are (1, 19) and (-1, -19). This concept helps visualize factor relationships and is especially useful for composite numbers.
12. Is 19 used in divisibility rules for other numbers?
While 19 itself does not have a commonly taught divisibility rule like 2, 3, or 5, it is a factor used in divisibility and factorization problems involving multiples of 19. Understanding 19's properties helps in higher-level math concepts and problem-solving.
