Highest Common Factor of 172, 785, 703 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 172, 785, 703 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 172, 785, 703 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 172, 785, 703 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 172, 785, 703 is 1.

HCF(172, 785, 703) = 1

HCF of 172, 785, 703 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 172, 785, 703 is 1.

Highest Common Factor of 172,785,703 using Euclid's algorithm

Highest Common Factor of 172,785,703 is 1

Step 1: Since 785 > 172, we apply the division lemma to 785 and 172, to get

785 = 172 x 4 + 97

Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 97 and 172, to get

172 = 97 x 1 + 75

Step 3: We consider the new divisor 97 and the new remainder 75, and apply the division lemma to get

97 = 75 x 1 + 22

We consider the new divisor 75 and the new remainder 22,and apply the division lemma to get

75 = 22 x 3 + 9

We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get

22 = 9 x 2 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 172 and 785 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(75,22) = HCF(97,75) = HCF(172,97) = HCF(785,172) .

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

Step 1: Since 703 > 1, we apply the division lemma to 703 and 1, to get

703 = 1 x 703 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 703 is 1

Notice that 1 = HCF(703,1) .

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Frequently Asked Questions on HCF of 172, 785, 703 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 172, 785, 703?

Answer: HCF of 172, 785, 703 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 172, 785, 703 using Euclid's Algorithm?

Answer: For arbitrary numbers 172, 785, 703 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.