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Factors of 19

Factors of 19 are the list of integers that can be evenly divided into 19. There are overall 2 factors of 19 among which 19 is the biggest factor and 1 and 19 are positive factors. The Prime Factors and Pair Factors of 19 are 1, 19, and (1, 19) respectively.

  • Factors of 19: 1 and 19
  • Negative Factors of 19: -1 and -19
  • Prime Factors of 19: 19
  • Prime Factorization of 19: 19
  • Sum of Factors of 19: 20
1. What Are the Factors of 19?
2. How to Calculate Factors of 19?
3. Factors of 19 by Prime Factorization
4. Factors of 19 in Pairs
5. Important Notes
6. FAQs on Factors of 19

What Are the Factors of 19?

A factor can be defined as a number that completely divides a given number. The factors of 19 are the numbers that exactly divide 19.

Factors of 19

Since 19 is a prime number, it has only two factors; they are 1 and 19.

How to Calculate the Factors of 19?

Factors of 19 are the numbers that multiply together to give the result as 19. Can you think of all such pairs of numbers? As mentioned before, only one such pair exists for the number 19. 19 is a prime number.

So, 19 can be written as 19 = 1 × 19

The number 19 has only two factors, the number itself and 1.

Hence, the factors of 19 are 1 and 19.

Explore factors using illustrations and interactive examples.

Factors of 19 by Prime Factorization

Prime factorization is a way of expressing a number as a product of its prime factors. The number 19 has a unique factorization because this is the only way it can be expressed: 19 = 1 × 19. This is the prime factorization of 19.

Factors of 18 can be found similarly. Let's see how:

When we write a number as a product of its factors, we say that the number has been factorized.

Let's see a few examples of prime factorization.

  • Prime factorization of 18

Factor Tree of 18

So, the prime factors of 18 are 3 and 2.

We can write 18 = 3 × 3 × 2

  • Prime factorization of 20

Factor tree of 20

So, the prime factors of 20 are 2 and 5.

We can write 20 = 2 ×2 × 5

Factors of 19 in Pairs

Factor pairs of 19 are the pairs of factors that, when multiplied together, give the product equal to the number 19. Like all other primes greater than 2, 19 has no factors apart from one and itself. So, it has a unique factor pair, that is, 1 and 19.

Important Notes:

  • The number 19 has only two factors, 1 and the number itself.
  • The prime factorization of 19 is 19 = 1 × 19
  • The number 19 has only one factor pair.
 

 

Factors of 19 Solved Examples

  1. Example 1: Sussane wants to decode the last two digits of the PIN of her ATM card. She knows that the number formed by the last two digits is a factor of 19 but not a factor of 36.

    Can you decode her PIN?

    Solution:

    Since 19 is a prime number, it has only two factors, 1 and 19.

    The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

    We observe that 19 is a factor of 19 but not a factor of 36.

    So, the required two-digit number is 19.

  2. Example 2: Jacky's teacher gave him a list of numbers: 23, 19, 20, 18, and 26. The teacher asked him a few questions as shown below. Which is the largest prime number on the list? How many common factors do 20 and 18 have? Which number has the largest prime factor in the list?

    Solution:

    There are only two prime numbers in this list, which are 19 and 23.

    23 is a prime number because the factors of 23 are 1 and the number itself.

    So, 23 is the largest prime number on the list.

    Let's calculate the factors of 20 and 18.

    Factors of 20: 1, 2, 4, 5, 10, and 20

    Factors of 18: 1, 2, 3, 6, 9, and 18

    So, numbers 20 and 18 have 2 common factors.

    Since 23 is the largest prime number in the list, it has the largest prime factor, i.e., 23.

  3. Example 3: Find the product of all the prime factors of 19.

    Solution:

    Since the prime factors of 19 are 19. Therefore, the product of prime factors = 19 = 19.

Show Solution >

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FAQs on Factors of 19

What are the Factors of 19?

The factors of 19 are 1, 19 and its negative factors are -1, -19.

What is the Greatest Common Factor of 19 and 14?

The factors of 19 are 1, 19 and the factors of 14 are 1, 2, 7, 14. 19 and 14 have only one common factor which is 1. This implies that 19 and 14 are co-prime.

Hence, the Greatest Common Factor (GCF) of 19 and 14 is 1.

What are the Common Factors of 19 and 17?

Since the factors of 19 are 1, 19, and factors of 17 are 1, 17. Hence, 19 and 17 have only one common factor which is 1. Therefore, 19 and 17 are co-prime.

What are the Prime Factors of 19?

The prime factor of 19 is 19.

What is the Sum of the Factors of 19?

Factors of 19 are 1, 19 and, the sum of all these factors is 1 + 19 = 20

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