Highest Common Factor of 176, 265, 670 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, 265, 670 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 176, 265, 670 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, 265, 670 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, 265, 670 is 1.

HCF(176, 265, 670) = 1

HCF of 176, 265, 670 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 176, 265, 670 is 1.

Highest Common Factor of 176,265,670 using Euclid's algorithm

Highest Common Factor of 176,265,670 is 1

Step 1: Since 265 > 176, we apply the division lemma to 265 and 176, to get

265 = 176 x 1 + 89

Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 89 and 176, to get

176 = 89 x 1 + 87

Step 3: We consider the new divisor 89 and the new remainder 87, and apply the division lemma to get

89 = 87 x 1 + 2

We consider the new divisor 87 and the new remainder 2,and apply the division lemma to get

87 = 2 x 43 + 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 176 and 265 is 1

Notice that 1 = HCF(2,1) = HCF(87,2) = HCF(89,87) = HCF(176,89) = HCF(265,176) .

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

Step 1: Since 670 > 1, we apply the division lemma to 670 and 1, to get

670 = 1 x 670 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 670 is 1

Notice that 1 = HCF(670,1) .

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Frequently Asked Questions on HCF of 176, 265, 670 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, 265, 670?

Answer: HCF of 176, 265, 670 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 176, 265, 670 using Euclid's Algorithm?

Answer: For arbitrary numbers 176, 265, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.