Highest Common Factor of 642, 994, 265 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 642, 994, 265 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 994, 265 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 642, 994, 265 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 642, 994, 265 is 1.

HCF(642, 994, 265) = 1

HCF of 642, 994, 265 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 642, 994, 265 is 1.

Highest Common Factor of 642,994,265 using Euclid's algorithm

Highest Common Factor of 642,994,265 is 1

Step 1: Since 994 > 642, we apply the division lemma to 994 and 642, to get

994 = 642 x 1 + 352

Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 352 and 642, to get

642 = 352 x 1 + 290

Step 3: We consider the new divisor 352 and the new remainder 290, and apply the division lemma to get

352 = 290 x 1 + 62

We consider the new divisor 290 and the new remainder 62,and apply the division lemma to get

290 = 62 x 4 + 42

We consider the new divisor 62 and the new remainder 42,and apply the division lemma to get

62 = 42 x 1 + 20

We consider the new divisor 42 and the new remainder 20,and apply the division lemma to get

42 = 20 x 2 + 2

We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get

20 = 2 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 642 and 994 is 2

Notice that 2 = HCF(20,2) = HCF(42,20) = HCF(62,42) = HCF(290,62) = HCF(352,290) = HCF(642,352) = HCF(994,642) .

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

Step 1: Since 265 > 2, we apply the division lemma to 265 and 2, to get

265 = 2 x 132 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 265 is 1

Notice that 1 = HCF(2,1) = HCF(265,2) .

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Frequently Asked Questions on HCF of 642, 994, 265 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 642, 994, 265?

Answer: HCF of 642, 994, 265 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 994, 265 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 994, 265 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.