Highest Common Factor of 65, 689, 719 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 65, 689, 719 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 65, 689, 719 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 65, 689, 719 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 65, 689, 719 is 1.

HCF(65, 689, 719) = 1

HCF of 65, 689, 719 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 65, 689, 719 is 1.

Highest Common Factor of 65,689,719 using Euclid's algorithm

Highest Common Factor of 65,689,719 is 1

Step 1: Since 689 > 65, we apply the division lemma to 689 and 65, to get

689 = 65 x 10 + 39

Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 39 and 65, to get

65 = 39 x 1 + 26

Step 3: We consider the new divisor 39 and the new remainder 26, and apply the division lemma to get

39 = 26 x 1 + 13

We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 65 and 689 is 13

Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(65,39) = HCF(689,65) .

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

Step 1: Since 719 > 13, we apply the division lemma to 719 and 13, to get

719 = 13 x 55 + 4

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 4 and 13, to get

13 = 4 x 3 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 719 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(719,13) .

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Frequently Asked Questions on HCF of 65, 689, 719 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 65, 689, 719?

Answer: HCF of 65, 689, 719 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 65, 689, 719 using Euclid's Algorithm?

Answer: For arbitrary numbers 65, 689, 719 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.