Highest Common Factor of 782, 8229, 5164 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 782, 8229, 5164 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 782, 8229, 5164 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 782, 8229, 5164 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 782, 8229, 5164 is 1.

HCF(782, 8229, 5164) = 1

HCF of 782, 8229, 5164 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 782, 8229, 5164 is 1.

Highest Common Factor of 782,8229,5164 using Euclid's algorithm

Highest Common Factor of 782,8229,5164 is 1

Step 1: Since 8229 > 782, we apply the division lemma to 8229 and 782, to get

8229 = 782 x 10 + 409

Step 2: Since the reminder 782 ≠ 0, we apply division lemma to 409 and 782, to get

782 = 409 x 1 + 373

Step 3: We consider the new divisor 409 and the new remainder 373, and apply the division lemma to get

409 = 373 x 1 + 36

We consider the new divisor 373 and the new remainder 36,and apply the division lemma to get

373 = 36 x 10 + 13

We consider the new divisor 36 and the new remainder 13,and apply the division lemma to get

36 = 13 x 2 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 782 and 8229 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(36,13) = HCF(373,36) = HCF(409,373) = HCF(782,409) = HCF(8229,782) .

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

Step 1: Since 5164 > 1, we apply the division lemma to 5164 and 1, to get

5164 = 1 x 5164 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5164 is 1

Notice that 1 = HCF(5164,1) .

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Frequently Asked Questions on HCF of 782, 8229, 5164 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 782, 8229, 5164?

Answer: HCF of 782, 8229, 5164 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 782, 8229, 5164 using Euclid's Algorithm?

Answer: For arbitrary numbers 782, 8229, 5164 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.