Highest Common Factor of 556, 992, 65 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 556, 992, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 556, 992, 65 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 556, 992, 65 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 556, 992, 65 is 1.

HCF(556, 992, 65) = 1

HCF of 556, 992, 65 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 556, 992, 65 is 1.

Highest Common Factor of 556,992,65 using Euclid's algorithm

Highest Common Factor of 556,992,65 is 1

Step 1: Since 992 > 556, we apply the division lemma to 992 and 556, to get

992 = 556 x 1 + 436

Step 2: Since the reminder 556 ≠ 0, we apply division lemma to 436 and 556, to get

556 = 436 x 1 + 120

Step 3: We consider the new divisor 436 and the new remainder 120, and apply the division lemma to get

436 = 120 x 3 + 76

We consider the new divisor 120 and the new remainder 76,and apply the division lemma to get

120 = 76 x 1 + 44

We consider the new divisor 76 and the new remainder 44,and apply the division lemma to get

76 = 44 x 1 + 32

We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get

44 = 32 x 1 + 12

We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get

32 = 12 x 2 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 556 and 992 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(76,44) = HCF(120,76) = HCF(436,120) = HCF(556,436) = HCF(992,556) .


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

Step 1: Since 65 > 4, we apply the division lemma to 65 and 4, to get

65 = 4 x 16 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 65 is 1

Notice that 1 = HCF(4,1) = HCF(65,4) .

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Frequently Asked Questions on HCF of 556, 992, 65 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 556, 992, 65?

Answer: HCF of 556, 992, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 556, 992, 65 using Euclid's Algorithm?

Answer: For arbitrary numbers 556, 992, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.