Highest Common Factor of 705, 638, 360 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 705, 638, 360 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 705, 638, 360 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 705, 638, 360 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 705, 638, 360 is 1.

HCF(705, 638, 360) = 1

HCF of 705, 638, 360 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 705, 638, 360 is 1.

Highest Common Factor of 705,638,360 using Euclid's algorithm

Highest Common Factor of 705,638,360 is 1

Step 1: Since 705 > 638, we apply the division lemma to 705 and 638, to get

705 = 638 x 1 + 67

Step 2: Since the reminder 638 ≠ 0, we apply division lemma to 67 and 638, to get

638 = 67 x 9 + 35

Step 3: We consider the new divisor 67 and the new remainder 35, and apply the division lemma to get

67 = 35 x 1 + 32

We consider the new divisor 35 and the new remainder 32,and apply the division lemma to get

35 = 32 x 1 + 3

We consider the new divisor 32 and the new remainder 3,and apply the division lemma to get

32 = 3 x 10 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 705 and 638 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) = HCF(35,32) = HCF(67,35) = HCF(638,67) = HCF(705,638) .

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

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

360 = 1 x 360 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 360 is 1

Notice that 1 = HCF(360,1) .

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Frequently Asked Questions on HCF of 705, 638, 360 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 705, 638, 360?

Answer: HCF of 705, 638, 360 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 705, 638, 360 using Euclid's Algorithm?

Answer: For arbitrary numbers 705, 638, 360 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.