Highest Common Factor of 708, 785, 205 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 708, 785, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 708, 785, 205 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 708, 785, 205 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 708, 785, 205 is 1.

HCF(708, 785, 205) = 1

HCF of 708, 785, 205 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 708, 785, 205 is 1.

Highest Common Factor of 708,785,205 using Euclid's algorithm

Highest Common Factor of 708,785,205 is 1

Step 1: Since 785 > 708, we apply the division lemma to 785 and 708, to get

785 = 708 x 1 + 77

Step 2: Since the reminder 708 ≠ 0, we apply division lemma to 77 and 708, to get

708 = 77 x 9 + 15

Step 3: We consider the new divisor 77 and the new remainder 15, and apply the division lemma to get

77 = 15 x 5 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 708 and 785 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(77,15) = HCF(708,77) = HCF(785,708) .

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

Step 1: Since 205 > 1, we apply the division lemma to 205 and 1, to get

205 = 1 x 205 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 205 is 1

Notice that 1 = HCF(205,1) .

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Frequently Asked Questions on HCF of 708, 785, 205 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 708, 785, 205?

Answer: HCF of 708, 785, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 708, 785, 205 using Euclid's Algorithm?

Answer: For arbitrary numbers 708, 785, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.