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HCF of 17, 23 and 29

HCF of 17, 23 and 29 is the largest possible number that divides 17, 23 and 29 exactly without any remainder. The factors of 17, 23 and 29 are (1, 17), (1, 23) and (1, 29) respectively. There are 3 commonly used methods to find the HCF of 17, 23 and 29 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 17, 23 and 29
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 17, 23 and 29?

Answer: HCF of 17, 23 and 29 is 1.

Explanation:

The HCF of three non-zero integers, x(17), y(23) and z(29), is the highest positive integer m(1) that divides x(17), y(23) and z(29) without any remainder.

Methods to Find HCF of 17, 23 and 29

The methods to find the HCF of 17, 23 and 29 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

HCF of 17, 23 and 29 by Long Division

HCF of 17, 23 and 29 can be represented as HCF of (HCF of 17, 23) and 29. HCF(17, 23, 29) can be thus calculated by first finding HCF(17, 23) using long division and thereafter using this result with 29 to perform long division again.

Step 1: Divide 23 (larger number) by 17 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (17) by the remainder (6). Repeat this process until the remainder = 0.
⇒ HCF(17, 23) = 1.
Step 3: Now to find the HCF of 1 and 29, we will perform a long division on 29 and 1.
Step 4: For remainder = 0, divisor = 1 ⇒ HCF(1, 29) = 1

Thus, HCF(17, 23, 29) = HCF(HCF(17, 23), 29) = 1.

HCF of 17, 23 and 29 by Prime Factorization

Prime factorization of 17, 23 and 29 is (17), (23) and (29) respectively. As visible, there are no common prime factors between 17, 23 and 29, i.e. they are co-prime. Hence, the HCF of 17, 23 and 29 will be 1.

HCF of 17, 23 and 29 by Listing Common Factors

Factors of 17: 1, 17
Factors of 23: 1, 23
Factors of 29: 1, 29

Since, 1 is the only common factor between 17, 23 and 29. The Highest Common Factor of 17, 23 and 29 is 1.

☛ Also Check:

HCF of 17, 23 and 29 Examples

Example 1: Find the highest number that divides 17, 23, and 29 completely.

Solution:

The highest number that divides 17, 23, and 29 exactly is their highest common factor.
- Factors of 17 = 1, 17
- Factors of 23 = 1, 23
- Factors of 29 = 1, 29
The HCF of 17, 23, and 29 is 1.
∴ The highest number that divides 17, 23, and 29 is 1.
Example 2: Calculate the HCF of 17, 23, and 29 using LCM of the given numbers.

Solution:

Prime factorization of 17, 23 and 29 is given as,
- 17 = 17
- 23 = 23
- 29 = 29
LCM(17, 23) = 391, LCM(23, 29) = 667, LCM(29, 17) = 493, LCM(17, 23, 29) = 11339
⇒ HCF(17, 23, 29) = [(17 × 23 × 29) × LCM(17, 23, 29)]/[LCM(17, 23) × LCM (23, 29) × LCM(29, 17)]
⇒ HCF(17, 23, 29) = (11339 × 11339)/(391 × 667 × 493)
⇒ HCF(17, 23, 29) = 1.
Therefore, the HCF of 17, 23 and 29 is 1.
Example 3: Verify the relation between the LCM and HCF of 17, 23 and 29.

Solution:

The relation between the LCM and HCF of 17, 23 and 29 is given as, HCF(17, 23, 29) = [(17 × 23 × 29) × LCM(17, 23, 29)]/[LCM(17, 23) × LCM (23, 29) × LCM(17, 29)]
⇒ Prime factorization of 17, 23 and 29:
- 17 = 17
- 23 = 23
- 29 = 29
∴ LCM of (17, 23), (23, 29), (17, 29), and (17, 23, 29) is 391, 667, 493, and 11339 respectively.
Now, LHS = HCF(17, 23, 29) = 1.
And, RHS = [(17 × 23 × 29) × LCM(17, 23, 29)]/[LCM(17, 23) × LCM (23, 29) × LCM(17, 29)] = [(11339) × 11339]/[391 × 667 × 493]
LHS = RHS = 1.
Hence verified.

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FAQs on HCF of 17, 23 and 29

What is the HCF of 17, 23 and 29?

The HCF of 17, 23 and 29 is 1. To calculate the highest common factor (HCF) of 17, 23 and 29, we need to factor each number (factors of 17 = 1, 17; factors of 23 = 1, 23; factors of 29 = 1, 29) and choose the highest factor that exactly divides 17, 23 and 29, i.e., 1.

What are the Methods to Find HCF of 17, 23 and 29?

There are three commonly used methods to find the HCF of 17, 23 and 29.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 17, 23 and 29 by Prime Factorization?

To find the HCF of 17, 23 and 29, we will find the prime factorization of given numbers, i.e. 17 = 17; 23 = 23; 29 = 29.
⇒ There is no common prime factor for 17, 23 and 29. Hence, HCF(17, 23, 29) = 1.
☛ Prime Number

Which of the following is HCF of 17, 23 and 29? 1, 67, 44, 71, 46, 57, 48, 74, 46

HCF of 17, 23, 29 will be the number that divides 17, 23, and 29 without leaving any remainder. The only number that satisfies the given condition is 1.

What is the Relation Between LCM and HCF of 17, 23 and 29?

The following equation can be used to express the relation between Least Common Multiple and HCF of 17, 23 and 29, i.e. HCF(17, 23, 29) = [(17 × 23 × 29) × LCM(17, 23, 29)]/[LCM(17, 23) × LCM (23, 29) × LCM(17, 29)].
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