Highest Common Factor of 862, 542, 89 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 862, 542, 89 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 862, 542, 89 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 862, 542, 89 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 862, 542, 89 is 1.

HCF(862, 542, 89) = 1

HCF of 862, 542, 89 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 862, 542, 89 is 1.

Highest Common Factor of 862,542,89 using Euclid's algorithm

Highest Common Factor of 862,542,89 is 1

Step 1: Since 862 > 542, we apply the division lemma to 862 and 542, to get

862 = 542 x 1 + 320

Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 320 and 542, to get

542 = 320 x 1 + 222

Step 3: We consider the new divisor 320 and the new remainder 222, and apply the division lemma to get

320 = 222 x 1 + 98

We consider the new divisor 222 and the new remainder 98,and apply the division lemma to get

222 = 98 x 2 + 26

We consider the new divisor 98 and the new remainder 26,and apply the division lemma to get

98 = 26 x 3 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 862 and 542 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(98,26) = HCF(222,98) = HCF(320,222) = HCF(542,320) = HCF(862,542) .

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

Step 1: Since 89 > 2, we apply the division lemma to 89 and 2, to get

89 = 2 x 44 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 89 is 1

Notice that 1 = HCF(2,1) = HCF(89,2) .

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Frequently Asked Questions on HCF of 862, 542, 89 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 862, 542, 89?

Answer: HCF of 862, 542, 89 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 862, 542, 89 using Euclid's Algorithm?

Answer: For arbitrary numbers 862, 542, 89 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.