Highest Common Factor of 420, 569, 896 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 420, 569, 896 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 569, 896 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 420, 569, 896 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 420, 569, 896 is 1.

HCF(420, 569, 896) = 1

HCF of 420, 569, 896 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 420, 569, 896 is 1.

Highest Common Factor of 420,569,896 using Euclid's algorithm

Highest Common Factor of 420,569,896 is 1

Step 1: Since 569 > 420, we apply the division lemma to 569 and 420, to get

569 = 420 x 1 + 149

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 149 and 420, to get

420 = 149 x 2 + 122

Step 3: We consider the new divisor 149 and the new remainder 122, and apply the division lemma to get

149 = 122 x 1 + 27

We consider the new divisor 122 and the new remainder 27,and apply the division lemma to get

122 = 27 x 4 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 420 and 569 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(122,27) = HCF(149,122) = HCF(420,149) = HCF(569,420) .

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

Step 1: Since 896 > 1, we apply the division lemma to 896 and 1, to get

896 = 1 x 896 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 896 is 1

Notice that 1 = HCF(896,1) .

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Frequently Asked Questions on HCF of 420, 569, 896 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 420, 569, 896?

Answer: HCF of 420, 569, 896 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 569, 896 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 569, 896 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.