Highest Common Factor of 560, 919 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, 919 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 919 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, 919 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, 919 is 1.

HCF(560, 919) = 1

HCF of 560, 919 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, 919 is 1.

Highest Common Factor of 560,919 using Euclid's algorithm

Highest Common Factor of 560,919 is 1

Step 1: Since 919 > 560, we apply the division lemma to 919 and 560, to get

919 = 560 x 1 + 359

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 359 and 560, to get

560 = 359 x 1 + 201

Step 3: We consider the new divisor 359 and the new remainder 201, and apply the division lemma to get

359 = 201 x 1 + 158

We consider the new divisor 201 and the new remainder 158,and apply the division lemma to get

201 = 158 x 1 + 43

We consider the new divisor 158 and the new remainder 43,and apply the division lemma to get

158 = 43 x 3 + 29

We consider the new divisor 43 and the new remainder 29,and apply the division lemma to get

43 = 29 x 1 + 14

We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get

29 = 14 x 2 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 560 and 919 is 1

Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(43,29) = HCF(158,43) = HCF(201,158) = HCF(359,201) = HCF(560,359) = HCF(919,560) .

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Frequently Asked Questions on HCF of 560, 919 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, 919?

Answer: HCF of 560, 919 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 919 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 919 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.