Highest Common Factor of 360, 679 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 360, 679 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 360, 679 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 360, 679 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 360, 679 is 1.

HCF(360, 679) = 1

HCF of 360, 679 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 360, 679 is 1.

Highest Common Factor of 360,679 using Euclid's algorithm

Highest Common Factor of 360,679 is 1

Step 1: Since 679 > 360, we apply the division lemma to 679 and 360, to get

679 = 360 x 1 + 319

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 319 and 360, to get

360 = 319 x 1 + 41

Step 3: We consider the new divisor 319 and the new remainder 41, and apply the division lemma to get

319 = 41 x 7 + 32

We consider the new divisor 41 and the new remainder 32,and apply the division lemma to get

41 = 32 x 1 + 9

We consider the new divisor 32 and the new remainder 9,and apply the division lemma to get

32 = 9 x 3 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 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 360 and 679 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(41,32) = HCF(319,41) = HCF(360,319) = HCF(679,360) .

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Frequently Asked Questions on HCF of 360, 679 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 360, 679?

Answer: HCF of 360, 679 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 360, 679 using Euclid's Algorithm?

Answer: For arbitrary numbers 360, 679 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.