Highest Common Factor of 990, 692, 571 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 990, 692, 571 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 990, 692, 571 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 990, 692, 571 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 990, 692, 571 is 1.

HCF(990, 692, 571) = 1

HCF of 990, 692, 571 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 990, 692, 571 is 1.

Highest Common Factor of 990,692,571 using Euclid's algorithm

Highest Common Factor of 990,692,571 is 1

Step 1: Since 990 > 692, we apply the division lemma to 990 and 692, to get

990 = 692 x 1 + 298

Step 2: Since the reminder 692 ≠ 0, we apply division lemma to 298 and 692, to get

692 = 298 x 2 + 96

Step 3: We consider the new divisor 298 and the new remainder 96, and apply the division lemma to get

298 = 96 x 3 + 10

We consider the new divisor 96 and the new remainder 10,and apply the division lemma to get

96 = 10 x 9 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 990 and 692 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(96,10) = HCF(298,96) = HCF(692,298) = HCF(990,692) .

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

Step 1: Since 571 > 2, we apply the division lemma to 571 and 2, to get

571 = 2 x 285 + 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 571 is 1

Notice that 1 = HCF(2,1) = HCF(571,2) .

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Frequently Asked Questions on HCF of 990, 692, 571 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 990, 692, 571?

Answer: HCF of 990, 692, 571 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 990, 692, 571 using Euclid's Algorithm?

Answer: For arbitrary numbers 990, 692, 571 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.