Highest Common Factor of 665, 355, 279 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, 355, 279 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 665, 355, 279 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, 355, 279 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, 355, 279 is 1.

HCF(665, 355, 279) = 1

HCF of 665, 355, 279 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, 355, 279 is 1.

Highest Common Factor of 665,355,279 using Euclid's algorithm

Highest Common Factor of 665,355,279 is 1

Step 1: Since 665 > 355, we apply the division lemma to 665 and 355, to get

665 = 355 x 1 + 310

Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 310 and 355, to get

355 = 310 x 1 + 45

Step 3: We consider the new divisor 310 and the new remainder 45, and apply the division lemma to get

310 = 45 x 6 + 40

We consider the new divisor 45 and the new remainder 40,and apply the division lemma to get

45 = 40 x 1 + 5

We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get

40 = 5 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 665 and 355 is 5

Notice that 5 = HCF(40,5) = HCF(45,40) = HCF(310,45) = HCF(355,310) = HCF(665,355) .

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

Step 1: Since 279 > 5, we apply the division lemma to 279 and 5, to get

279 = 5 x 55 + 4

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get

5 = 4 x 1 + 1

Step 3: 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 5 and 279 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(279,5) .

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Frequently Asked Questions on HCF of 665, 355, 279 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, 355, 279?

Answer: HCF of 665, 355, 279 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 665, 355, 279 using Euclid's Algorithm?

Answer: For arbitrary numbers 665, 355, 279 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.