Highest Common Factor of 562, 870, 854 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 562, 870, 854 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 562, 870, 854 is 2 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 562, 870, 854 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 562, 870, 854 is 2.

HCF(562, 870, 854) = 2

HCF of 562, 870, 854 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 562, 870, 854 is 2.

Highest Common Factor of 562,870,854 using Euclid's algorithm

Highest Common Factor of 562,870,854 is 2

Step 1: Since 870 > 562, we apply the division lemma to 870 and 562, to get

870 = 562 x 1 + 308

Step 2: Since the reminder 562 ≠ 0, we apply division lemma to 308 and 562, to get

562 = 308 x 1 + 254

Step 3: We consider the new divisor 308 and the new remainder 254, and apply the division lemma to get

308 = 254 x 1 + 54

We consider the new divisor 254 and the new remainder 54,and apply the division lemma to get

254 = 54 x 4 + 38

We consider the new divisor 54 and the new remainder 38,and apply the division lemma to get

54 = 38 x 1 + 16

We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get

38 = 16 x 2 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 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 562 and 870 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(54,38) = HCF(254,54) = HCF(308,254) = HCF(562,308) = HCF(870,562) .

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

Step 1: Since 854 > 2, we apply the division lemma to 854 and 2, to get

854 = 2 x 427 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 854 is 2

Notice that 2 = HCF(854,2) .

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Frequently Asked Questions on HCF of 562, 870, 854 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 562, 870, 854?

Answer: HCF of 562, 870, 854 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 562, 870, 854 using Euclid's Algorithm?

Answer: For arbitrary numbers 562, 870, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.