Highest Common Factor of 34, 85, 69 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 34, 85, 69 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 34, 85, 69 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 34, 85, 69 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 34, 85, 69 is 1.

HCF(34, 85, 69) = 1

HCF of 34, 85, 69 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 34, 85, 69 is 1.

Highest Common Factor of 34,85,69 using Euclid's algorithm

Highest Common Factor of 34,85,69 is 1

Step 1: Since 85 > 34, we apply the division lemma to 85 and 34, to get

85 = 34 x 2 + 17

Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 17 and 34, to get

34 = 17 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 34 and 85 is 17

Notice that 17 = HCF(34,17) = HCF(85,34) .


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

Step 1: Since 69 > 17, we apply the division lemma to 69 and 17, to get

69 = 17 x 4 + 1

Step 2: Since the reminder 17 ≠ 0, we apply division lemma to 1 and 17, to get

17 = 1 x 17 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 17 and 69 is 1

Notice that 1 = HCF(17,1) = HCF(69,17) .

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Frequently Asked Questions on HCF of 34, 85, 69 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 34, 85, 69?

Answer: HCF of 34, 85, 69 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 34, 85, 69 using Euclid's Algorithm?

Answer: For arbitrary numbers 34, 85, 69 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.