Highest Common Factor of 690, 360, 623 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 690, 360, 623 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 690, 360, 623 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 690, 360, 623 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 690, 360, 623 is 1.

HCF(690, 360, 623) = 1

HCF of 690, 360, 623 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 690, 360, 623 is 1.

Highest Common Factor of 690,360,623 using Euclid's algorithm

Highest Common Factor of 690,360,623 is 1

Step 1: Since 690 > 360, we apply the division lemma to 690 and 360, to get

690 = 360 x 1 + 330

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 330 and 360, to get

360 = 330 x 1 + 30

Step 3: We consider the new divisor 330 and the new remainder 30, and apply the division lemma to get

330 = 30 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 690 and 360 is 30

Notice that 30 = HCF(330,30) = HCF(360,330) = HCF(690,360) .

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

Step 1: Since 623 > 30, we apply the division lemma to 623 and 30, to get

623 = 30 x 20 + 23

Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 23 and 30, to get

30 = 23 x 1 + 7

Step 3: We consider the new divisor 23 and the new remainder 7, and apply the division lemma to get

23 = 7 x 3 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 30 and 623 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(30,23) = HCF(623,30) .

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Frequently Asked Questions on HCF of 690, 360, 623 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 690, 360, 623?

Answer: HCF of 690, 360, 623 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 690, 360, 623 using Euclid's Algorithm?

Answer: For arbitrary numbers 690, 360, 623 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.