Highest Common Factor of 642, 999, 678 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, 999, 678 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 999, 678 is 3 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, 999, 678 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, 999, 678 is 3.

HCF(642, 999, 678) = 3

HCF of 642, 999, 678 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, 999, 678 is 3.

Highest Common Factor of 642,999,678 using Euclid's algorithm

Highest Common Factor of 642,999,678 is 3

Step 1: Since 999 > 642, we apply the division lemma to 999 and 642, to get

999 = 642 x 1 + 357

Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 357 and 642, to get

642 = 357 x 1 + 285

Step 3: We consider the new divisor 357 and the new remainder 285, and apply the division lemma to get

357 = 285 x 1 + 72

We consider the new divisor 285 and the new remainder 72,and apply the division lemma to get

285 = 72 x 3 + 69

We consider the new divisor 72 and the new remainder 69,and apply the division lemma to get

72 = 69 x 1 + 3

We consider the new divisor 69 and the new remainder 3,and apply the division lemma to get

69 = 3 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 642 and 999 is 3

Notice that 3 = HCF(69,3) = HCF(72,69) = HCF(285,72) = HCF(357,285) = HCF(642,357) = HCF(999,642) .

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

Step 1: Since 678 > 3, we apply the division lemma to 678 and 3, to get

678 = 3 x 226 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 678 is 3

Notice that 3 = HCF(678,3) .

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Frequently Asked Questions on HCF of 642, 999, 678 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, 999, 678?

Answer: HCF of 642, 999, 678 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 999, 678 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 999, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.