Highest Common Factor of 176, 236, 735 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 176, 236, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 176, 236, 735 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 176, 236, 735 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 176, 236, 735 is 1.

HCF(176, 236, 735) = 1

HCF of 176, 236, 735 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 176, 236, 735 is 1.

Highest Common Factor of 176,236,735 using Euclid's algorithm

Highest Common Factor of 176,236,735 is 1

Step 1: Since 236 > 176, we apply the division lemma to 236 and 176, to get

236 = 176 x 1 + 60

Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 60 and 176, to get

176 = 60 x 2 + 56

Step 3: We consider the new divisor 60 and the new remainder 56, and apply the division lemma to get

60 = 56 x 1 + 4

We consider the new divisor 56 and the new remainder 4, and apply the division lemma to get

56 = 4 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 176 and 236 is 4

Notice that 4 = HCF(56,4) = HCF(60,56) = HCF(176,60) = HCF(236,176) .

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

Step 1: Since 735 > 4, we apply the division lemma to 735 and 4, to get

735 = 4 x 183 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 735 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(735,4) .

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Frequently Asked Questions on HCF of 176, 236, 735 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 176, 236, 735?

Answer: HCF of 176, 236, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 176, 236, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 176, 236, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.