Highest Common Factor of 563, 966, 74 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 563, 966, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 563, 966, 74 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 563, 966, 74 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 563, 966, 74 is 1.

HCF(563, 966, 74) = 1

HCF of 563, 966, 74 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 563, 966, 74 is 1.

Highest Common Factor of 563,966,74 using Euclid's algorithm

Highest Common Factor of 563,966,74 is 1

Step 1: Since 966 > 563, we apply the division lemma to 966 and 563, to get

966 = 563 x 1 + 403

Step 2: Since the reminder 563 ≠ 0, we apply division lemma to 403 and 563, to get

563 = 403 x 1 + 160

Step 3: We consider the new divisor 403 and the new remainder 160, and apply the division lemma to get

403 = 160 x 2 + 83

We consider the new divisor 160 and the new remainder 83,and apply the division lemma to get

160 = 83 x 1 + 77

We consider the new divisor 83 and the new remainder 77,and apply the division lemma to get

83 = 77 x 1 + 6

We consider the new divisor 77 and the new remainder 6,and apply the division lemma to get

77 = 6 x 12 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 563 and 966 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(77,6) = HCF(83,77) = HCF(160,83) = HCF(403,160) = HCF(563,403) = HCF(966,563) .

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

Step 1: Since 74 > 1, we apply the division lemma to 74 and 1, to get

74 = 1 x 74 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 74 is 1

Notice that 1 = HCF(74,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 563, 966, 74 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 563, 966, 74?

Answer: HCF of 563, 966, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 563, 966, 74 using Euclid's Algorithm?

Answer: For arbitrary numbers 563, 966, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.