Highest Common Factor of 174, 692, 969 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, 692, 969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 174, 692, 969 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, 692, 969 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, 692, 969 is 1.

HCF(174, 692, 969) = 1

HCF of 174, 692, 969 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, 692, 969 is 1.

Highest Common Factor of 174,692,969 using Euclid's algorithm

Highest Common Factor of 174,692,969 is 1

Step 1: Since 692 > 174, we apply the division lemma to 692 and 174, to get

692 = 174 x 3 + 170

Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 170 and 174, to get

174 = 170 x 1 + 4

Step 3: We consider the new divisor 170 and the new remainder 4, and apply the division lemma to get

170 = 4 x 42 + 2

We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 174 and 692 is 2

Notice that 2 = HCF(4,2) = HCF(170,4) = HCF(174,170) = HCF(692,174) .

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

Step 1: Since 969 > 2, we apply the division lemma to 969 and 2, to get

969 = 2 x 484 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 969 is 1

Notice that 1 = HCF(2,1) = HCF(969,2) .

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, 692, 969 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, 692, 969?

Answer: HCF of 174, 692, 969 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 174, 692, 969 using Euclid's Algorithm?

Answer: For arbitrary numbers 174, 692, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.