Highest Common Factor of 417, 780, 720, 34 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 417, 780, 720, 34 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 417, 780, 720, 34 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 417, 780, 720, 34 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 417, 780, 720, 34 is 1.

HCF(417, 780, 720, 34) = 1

HCF of 417, 780, 720, 34 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 417, 780, 720, 34 is 1.

Highest Common Factor of 417,780,720,34 using Euclid's algorithm

Highest Common Factor of 417,780,720,34 is 1

Step 1: Since 780 > 417, we apply the division lemma to 780 and 417, to get

780 = 417 x 1 + 363

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 363 and 417, to get

417 = 363 x 1 + 54

Step 3: We consider the new divisor 363 and the new remainder 54, and apply the division lemma to get

363 = 54 x 6 + 39

We consider the new divisor 54 and the new remainder 39,and apply the division lemma to get

54 = 39 x 1 + 15

We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get

39 = 15 x 2 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 417 and 780 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(54,39) = HCF(363,54) = HCF(417,363) = HCF(780,417) .

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

Step 1: Since 720 > 3, we apply the division lemma to 720 and 3, to get

720 = 3 x 240 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 720 is 3

Notice that 3 = HCF(720,3) .

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

Step 1: Since 34 > 3, we apply the division lemma to 34 and 3, to get

34 = 3 x 11 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 34 is 1

Notice that 1 = HCF(3,1) = HCF(34,3) .

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Frequently Asked Questions on HCF of 417, 780, 720, 34 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 417, 780, 720, 34?

Answer: HCF of 417, 780, 720, 34 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 417, 780, 720, 34 using Euclid's Algorithm?

Answer: For arbitrary numbers 417, 780, 720, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.