Highest Common Factor of 560, 407, 218 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, 407, 218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 407, 218 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, 407, 218 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, 407, 218 is 1.

HCF(560, 407, 218) = 1

HCF of 560, 407, 218 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, 407, 218 is 1.

Highest Common Factor of 560,407,218 using Euclid's algorithm

Highest Common Factor of 560,407,218 is 1

Step 1: Since 560 > 407, we apply the division lemma to 560 and 407, to get

560 = 407 x 1 + 153

Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 153 and 407, to get

407 = 153 x 2 + 101

Step 3: We consider the new divisor 153 and the new remainder 101, and apply the division lemma to get

153 = 101 x 1 + 52

We consider the new divisor 101 and the new remainder 52,and apply the division lemma to get

101 = 52 x 1 + 49

We consider the new divisor 52 and the new remainder 49,and apply the division lemma to get

52 = 49 x 1 + 3

We consider the new divisor 49 and the new remainder 3,and apply the division lemma to get

49 = 3 x 16 + 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 560 and 407 is 1

Notice that 1 = HCF(3,1) = HCF(49,3) = HCF(52,49) = HCF(101,52) = HCF(153,101) = HCF(407,153) = HCF(560,407) .

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

Step 1: Since 218 > 1, we apply the division lemma to 218 and 1, to get

218 = 1 x 218 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 218 is 1

Notice that 1 = HCF(218,1) .

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Frequently Asked Questions on HCF of 560, 407, 218 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, 407, 218?

Answer: HCF of 560, 407, 218 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 407, 218 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 407, 218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.