Highest Common Factor of 645, 346, 772, 403 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 645, 346, 772, 403 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 645, 346, 772, 403 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 645, 346, 772, 403 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 645, 346, 772, 403 is 1.

HCF(645, 346, 772, 403) = 1

HCF of 645, 346, 772, 403 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 645, 346, 772, 403 is 1.

Highest Common Factor of 645,346,772,403 using Euclid's algorithm

Highest Common Factor of 645,346,772,403 is 1

Step 1: Since 645 > 346, we apply the division lemma to 645 and 346, to get

645 = 346 x 1 + 299

Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 299 and 346, to get

346 = 299 x 1 + 47

Step 3: We consider the new divisor 299 and the new remainder 47, and apply the division lemma to get

299 = 47 x 6 + 17

We consider the new divisor 47 and the new remainder 17,and apply the division lemma to get

47 = 17 x 2 + 13

We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get

17 = 13 x 1 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

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 645 and 346 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(47,17) = HCF(299,47) = HCF(346,299) = HCF(645,346) .

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

Step 1: Since 772 > 1, we apply the division lemma to 772 and 1, to get

772 = 1 x 772 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 772 is 1

Notice that 1 = HCF(772,1) .

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

Step 1: Since 403 > 1, we apply the division lemma to 403 and 1, to get

403 = 1 x 403 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 403 is 1

Notice that 1 = HCF(403,1) .

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Frequently Asked Questions on HCF of 645, 346, 772, 403 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 645, 346, 772, 403?

Answer: HCF of 645, 346, 772, 403 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 645, 346, 772, 403 using Euclid's Algorithm?

Answer: For arbitrary numbers 645, 346, 772, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.