Highest Common Factor of 178, 749, 923 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 178, 749, 923 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 178, 749, 923 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 178, 749, 923 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 178, 749, 923 is 1.

HCF(178, 749, 923) = 1

HCF of 178, 749, 923 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 178, 749, 923 is 1.

Highest Common Factor of 178,749,923 using Euclid's algorithm

Highest Common Factor of 178,749,923 is 1

Step 1: Since 749 > 178, we apply the division lemma to 749 and 178, to get

749 = 178 x 4 + 37

Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 37 and 178, to get

178 = 37 x 4 + 30

Step 3: We consider the new divisor 37 and the new remainder 30, and apply the division lemma to get

37 = 30 x 1 + 7

We consider the new divisor 30 and the new remainder 7,and apply the division lemma to get

30 = 7 x 4 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 178 and 749 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(30,7) = HCF(37,30) = HCF(178,37) = HCF(749,178) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 923 > 1, we apply the division lemma to 923 and 1, to get

923 = 1 x 923 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 923 is 1

Notice that 1 = HCF(923,1) .

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Frequently Asked Questions on HCF of 178, 749, 923 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 178, 749, 923?

Answer: HCF of 178, 749, 923 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 178, 749, 923 using Euclid's Algorithm?

Answer: For arbitrary numbers 178, 749, 923 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.