Find the LCM and HCF of the integers 17,23 and 29 by applying the prime factorisation Method

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.

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

1. 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.

2. 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,

   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.

Show Solution >

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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)].
☛ Highest Common Factor Calculator

The largest possible number which divides the given numbers exactly without any remainder is called the highest common factor of the given numbers.

Least Common Multiple  of a and b is the smallest number that divides a and b exactly

Answer: (1) LCM(12, 15, 21) = 420, HCF(12, 15, 21) = 3 (2) LCM(17, 23, 29) = 11339, HCF(17, 23, 29) = 1 (3) LCM(8, 9, 25) = 1800, HCF(8, 9, 25) = 1.  

Let's look into the prime factorization method to calculate the HCF and LCM

Explanation:

Follow the steps mentioned below to find the LCM of the given integer.

Step 1: Write down the prime factorization of each integer.

Step 2: Write the prime factorization of each integer in exponential form and select the highest power of all the factors that occur in any of these numbers.

Step 3: Find the product of factors found in step 2.

Follow the steps mentioned below to find the HCF of the given integer.

Step 1: Write down the prime factorization of each integer.

Step 2: Write the common factors of each integer.

Step 3: Find the product of factors found in step 2.

(1)

Prime factorization of 12: 2 × 2 × 3 = 22 × 3

Prime factorization of 15: 3 × 5

Prime factorization of 21: 3 × 7

LCM of 12, 15, and 21 is given as:

LCM(12, 15, 21) = 22 × 3 × 5 × 7 = 4 × 3 × 5 × 7 = 420

HCF of 12, 15, and 21 is given as:

Common factors of the three numbers are: 3

HCF(12, 15, 21) = 3

(2)

Prime factorization of 17: 17

Prime factorization of 23: 23

Prime factorization of 29: 29

LCM of 17, 23, and 29 is given as:

LCM(17, 23, 29) = 17 × 23 × 29 = 11339

HCF of 17, 23, and 29 is given as:

Since there's not any common factor

Hence, HCF(17, 23, 29) = 1

(3)

Prime factorization of 8: 2 × 2 × 2 = 23

Prime factorization of 9: 3 × 3 = 32

Prime factorization of 25: 5 × 5 = 52

LCM of 8, 9, and 25 is given as:

LCM(8, 9, 25) = 23 × 32 × 52 = 8 × 9 × 25 =1800

HCF of 8, 9, and 25 is given as:

Since there's no common factor

Hence, HCF(8, 9, 25) = 1

Thus, (1) LCM(12, 15, 21) = 420, HCF(12, 15, 21) = 3 (2) LCM(17, 23, 29) = 11339, HCF(17, 23, 29) = 1 (3) LCM(8, 9, 25) = 1800, HCF(8, 9, 25) = 1.

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