Highest Common Factor of 560, 335, 829 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 560, 335, 829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 335, 829 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 560, 335, 829 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 560, 335, 829 is 1.

HCF(560, 335, 829) = 1

HCF of 560, 335, 829 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 560, 335, 829 is 1.

Highest Common Factor of 560,335,829 using Euclid's algorithm

Highest Common Factor of 560,335,829 is 1

Step 1: Since 560 > 335, we apply the division lemma to 560 and 335, to get

560 = 335 x 1 + 225

Step 2: Since the reminder 335 ≠ 0, we apply division lemma to 225 and 335, to get

335 = 225 x 1 + 110

Step 3: We consider the new divisor 225 and the new remainder 110, and apply the division lemma to get

225 = 110 x 2 + 5

We consider the new divisor 110 and the new remainder 5, and apply the division lemma to get

110 = 5 x 22 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 560 and 335 is 5

Notice that 5 = HCF(110,5) = HCF(225,110) = HCF(335,225) = HCF(560,335) .

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

Step 1: Since 829 > 5, we apply the division lemma to 829 and 5, to get

829 = 5 x 165 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: 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 5 and 829 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(829,5) .

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Frequently Asked Questions on HCF of 560, 335, 829 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 560, 335, 829?

Answer: HCF of 560, 335, 829 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 335, 829 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 335, 829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.