Highest Common Factor of 638, 991, 212, 56 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 638, 991, 212, 56 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 638, 991, 212, 56 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 638, 991, 212, 56 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 638, 991, 212, 56 is 1.

HCF(638, 991, 212, 56) = 1

HCF of 638, 991, 212, 56 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 638, 991, 212, 56 is 1.

Highest Common Factor of 638,991,212,56 using Euclid's algorithm

Highest Common Factor of 638,991,212,56 is 1

Step 1: Since 991 > 638, we apply the division lemma to 991 and 638, to get

991 = 638 x 1 + 353

Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 353 and 638, to get

638 = 353 x 1 + 285

Step 3: We consider the new divisor 353 and the new remainder 285, and apply the division lemma to get

353 = 285 x 1 + 68

We consider the new divisor 285 and the new remainder 68,and apply the division lemma to get

285 = 68 x 4 + 13

We consider the new divisor 68 and the new remainder 13,and apply the division lemma to get

68 = 13 x 5 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 638 and 991 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(68,13) = HCF(285,68) = HCF(353,285) = HCF(638,353) = HCF(991,638) .

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

Step 1: Since 212 > 1, we apply the division lemma to 212 and 1, to get

212 = 1 x 212 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 212 is 1

Notice that 1 = HCF(212,1) .

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

Step 1: Since 56 > 1, we apply the division lemma to 56 and 1, to get

56 = 1 x 56 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 56 is 1

Notice that 1 = HCF(56,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 638, 991, 212, 56 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 638, 991, 212, 56?

Answer: HCF of 638, 991, 212, 56 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 638, 991, 212, 56 using Euclid's Algorithm?

Answer: For arbitrary numbers 638, 991, 212, 56 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.