Highest Common Factor of 665, 914, 474 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 665, 914, 474 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 914, 474 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 665, 914, 474 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 665, 914, 474 is 1.

HCF(665, 914, 474) = 1

HCF of 665, 914, 474 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 665, 914, 474 is 1.

Highest Common Factor of 665,914,474 using Euclid's algorithm

Highest Common Factor of 665,914,474 is 1

Step 1: Since 914 > 665, we apply the division lemma to 914 and 665, to get

914 = 665 x 1 + 249

Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 249 and 665, to get

665 = 249 x 2 + 167

Step 3: We consider the new divisor 249 and the new remainder 167, and apply the division lemma to get

249 = 167 x 1 + 82

We consider the new divisor 167 and the new remainder 82,and apply the division lemma to get

167 = 82 x 2 + 3

We consider the new divisor 82 and the new remainder 3,and apply the division lemma to get

82 = 3 x 27 + 1

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 665 and 914 is 1

Notice that 1 = HCF(3,1) = HCF(82,3) = HCF(167,82) = HCF(249,167) = HCF(665,249) = HCF(914,665) .

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

Step 1: Since 474 > 1, we apply the division lemma to 474 and 1, to get

474 = 1 x 474 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 474 is 1

Notice that 1 = HCF(474,1) .

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Frequently Asked Questions on HCF of 665, 914, 474 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 665, 914, 474?

Answer: HCF of 665, 914, 474 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 914, 474 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 914, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.