Highest Common Factor of 623, 369, 198 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 623, 369, 198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 623, 369, 198 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 623, 369, 198 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 623, 369, 198 is 1.

HCF(623, 369, 198) = 1

HCF of 623, 369, 198 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 623, 369, 198 is 1.

Highest Common Factor of 623,369,198 using Euclid's algorithm

Highest Common Factor of 623,369,198 is 1

Step 1: Since 623 > 369, we apply the division lemma to 623 and 369, to get

623 = 369 x 1 + 254

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 254 and 369, to get

369 = 254 x 1 + 115

Step 3: We consider the new divisor 254 and the new remainder 115, and apply the division lemma to get

254 = 115 x 2 + 24

We consider the new divisor 115 and the new remainder 24,and apply the division lemma to get

115 = 24 x 4 + 19

We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get

24 = 19 x 1 + 5

We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get

19 = 5 x 3 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 623 and 369 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(115,24) = HCF(254,115) = HCF(369,254) = HCF(623,369) .

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

Step 1: Since 198 > 1, we apply the division lemma to 198 and 1, to get

198 = 1 x 198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 198 is 1

Notice that 1 = HCF(198,1) .

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Frequently Asked Questions on HCF of 623, 369, 198 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 623, 369, 198?

Answer: HCF of 623, 369, 198 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 623, 369, 198 using Euclid's Algorithm?

Answer: For arbitrary numbers 623, 369, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.