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HCF of 13 and 19

HCF of 13 and 19 is the largest possible number that divides 13 and 19 exactly without any remainder. The factors of 13 and 19 are 1, 13 and 1, 19 respectively. There are 3 commonly used methods to find the HCF of 13 and 19 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 13 and 19
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 13 and 19?

Answer: HCF of 13 and 19 is 1.

Explanation:

The HCF of two non-zero integers, x(13) and y(19), is the highest positive integer m(1) that divides both x(13) and y(19) without any remainder.

Methods to Find HCF of 13 and 19

The methods to find the HCF of 13 and 19 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 13 and 19 by Prime Factorization

Prime factorization of 13 and 19 is (13) and (19) respectively. As visible, there are no common prime factors between 13 and 19, i.e. they are co-prime. Hence, the HCF of 13 and 19 will be 1.

HCF of 13 and 19 by Listing Common Factors

Factors of 13: 1, 13
Factors of 19: 1, 19

Since, 1 is the only common factor between 13 and 19. The highest common factor of 13 and 19 is 1.

HCF of 13 and 19 by Long Division

HCF of 13 and 19 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 19 (larger number) by 13 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (13) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 13 and 19.

☛ Also Check:

HCF of 13 and 19 Examples

Example 1: Find the highest number that divides 13 and 19 exactly.

Solution:

The highest number that divides 13 and 19 exactly is their highest common factor, i.e. HCF of 13 and 19.
⇒ Factors of 13 and 19:
- Factors of 13 = 1, 13
- Factors of 19 = 1, 19
Therefore, the HCF of 13 and 19 is 1.
Example 2: Find the HCF of 13 and 19, if their LCM is 247.

Solution:

∵ LCM × HCF = 13 × 19
⇒ HCF(13, 19) = (13 × 19)/247 = 1
Therefore, the highest common factor of 13 and 19 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 247. If one number is 19, find the other number.

Solution:

Given: HCF (y, 19) = 1 and LCM (y, 19) = 247
∵ HCF × LCM = 19 × (y)
⇒ y = (HCF × LCM)/19
⇒ y = (1 × 247)/19
⇒ y = 13
Therefore, the other number is 13.

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FAQs on HCF of 13 and 19

What is the HCF of 13 and 19?

The HCF of 13 and 19 is 1. To calculate the Highest common factor (HCF) of 13 and 19, we need to factor each number (factors of 13 = 1, 13; factors of 19 = 1, 19) and choose the highest factor that exactly divides both 13 and 19, i.e., 1.

If the HCF of 19 and 13 is 1, Find its LCM.

HCF(19, 13) × LCM(19, 13) = 19 × 13
Since the HCF of 19 and 13 = 1
⇒ 1 × LCM(19, 13) = 247
Therefore, LCM = 247
☛ HCF Calculator

How to Find the HCF of 13 and 19 by Prime Factorization?

To find the HCF of 13 and 19, we will find the prime factorization of the given numbers, i.e. 13 = 13; 19 = 19.
⇒ There is no common prime factor for 13 and 19. Hence, HCF (13, 19) = 1.
☛ What is a Prime Number?

What are the Methods to Find HCF of 13 and 19?

There are three commonly used methods to find the HCF of 13 and 19.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the HCF of 13 and 19 by Long Division Method?

To find the HCF of 13, 19 using long division method, 19 is divided by 13. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 13, 19?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 13 and 19, i.e. HCF × LCM = 13 × 19.

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