Highest Common Factor of 996, 588, 640 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 996, 588, 640 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 996, 588, 640 is 4 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 996, 588, 640 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 996, 588, 640 is 4.

HCF(996, 588, 640) = 4

HCF of 996, 588, 640 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 996, 588, 640 is 4.

Highest Common Factor of 996,588,640 using Euclid's algorithm

Highest Common Factor of 996,588,640 is 4

Step 1: Since 996 > 588, we apply the division lemma to 996 and 588, to get

996 = 588 x 1 + 408

Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 408 and 588, to get

588 = 408 x 1 + 180

Step 3: We consider the new divisor 408 and the new remainder 180, and apply the division lemma to get

408 = 180 x 2 + 48

We consider the new divisor 180 and the new remainder 48,and apply the division lemma to get

180 = 48 x 3 + 36

We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get

48 = 36 x 1 + 12

We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get

36 = 12 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 996 and 588 is 12

Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(180,48) = HCF(408,180) = HCF(588,408) = HCF(996,588) .

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

Step 1: Since 640 > 12, we apply the division lemma to 640 and 12, to get

640 = 12 x 53 + 4

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 4 and 12, to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 12 and 640 is 4

Notice that 4 = HCF(12,4) = HCF(640,12) .

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Frequently Asked Questions on HCF of 996, 588, 640 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 996, 588, 640?

Answer: HCF of 996, 588, 640 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 996, 588, 640 using Euclid's Algorithm?

Answer: For arbitrary numbers 996, 588, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.