Highest Common Factor of 344, 598, 765 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 344, 598, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 344, 598, 765 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 344, 598, 765 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 344, 598, 765 is 1.

HCF(344, 598, 765) = 1

HCF of 344, 598, 765 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 344, 598, 765 is 1.

Highest Common Factor of 344,598,765 using Euclid's algorithm

Highest Common Factor of 344,598,765 is 1

Step 1: Since 598 > 344, we apply the division lemma to 598 and 344, to get

598 = 344 x 1 + 254

Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 254 and 344, to get

344 = 254 x 1 + 90

Step 3: We consider the new divisor 254 and the new remainder 90, and apply the division lemma to get

254 = 90 x 2 + 74

We consider the new divisor 90 and the new remainder 74,and apply the division lemma to get

90 = 74 x 1 + 16

We consider the new divisor 74 and the new remainder 16,and apply the division lemma to get

74 = 16 x 4 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 344 and 598 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(74,16) = HCF(90,74) = HCF(254,90) = HCF(344,254) = HCF(598,344) .

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

Step 1: Since 765 > 2, we apply the division lemma to 765 and 2, to get

765 = 2 x 382 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 765 is 1

Notice that 1 = HCF(2,1) = HCF(765,2) .

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Frequently Asked Questions on HCF of 344, 598, 765 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 344, 598, 765?

Answer: HCF of 344, 598, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 344, 598, 765 using Euclid's Algorithm?

Answer: For arbitrary numbers 344, 598, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.