HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 34, 51, 85 i.e. 17 the largest integer that leaves a remainder zero for all numbers.

HCF of 34, 51, 85 is 17 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, 51, 85 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, 51, 85 is **17**.

HCF(34, 51, 85) = 17

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

Highest common factor (HCF) of 34, 51, 85 is **17**.

**Step 1:** Since 51 > 34, we apply the division lemma to 51 and 34, to get

51 = 34 x 1 + 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 51 is 17

Notice that 17 = HCF(34,17) = HCF(51,34) .

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

**Step 1:** Since 85 > 17, we apply the division lemma to 85 and 17, to get

85 = 17 x 5 + 0

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

Notice that 17 = HCF(85,17) .

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

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, 51, 85?

Answer: HCF of 34, 51, 85 is 17 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 34, 51, 85 using Euclid's Algorithm?

Answer: For arbitrary numbers 34, 51, 85 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.