Highest Common Factor of 174, 385, 178 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 174, 385, 178 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 174, 385, 178 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 174, 385, 178 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 174, 385, 178 is 1.

HCF(174, 385, 178) = 1

HCF of 174, 385, 178 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 174, 385, 178 is 1.

Highest Common Factor of 174,385,178 using Euclid's algorithm

Highest Common Factor of 174,385,178 is 1

Step 1: Since 385 > 174, we apply the division lemma to 385 and 174, to get

385 = 174 x 2 + 37

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 37 and 174, to get

174 = 37 x 4 + 26

Step 3: We consider the new divisor 37 and the new remainder 26, and apply the division lemma to get

37 = 26 x 1 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 174 and 385 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(37,26) = HCF(174,37) = HCF(385,174) .

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

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

178 = 1 x 178 + 0

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

Notice that 1 = HCF(178,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 174, 385, 178 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 174, 385, 178?

Answer: HCF of 174, 385, 178 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 174, 385, 178 using Euclid's Algorithm?

Answer: For arbitrary numbers 174, 385, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.