Highest Common Factor of 992, 574, 470 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 992, 574, 470 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 992, 574, 470 is 2 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 992, 574, 470 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 992, 574, 470 is 2.

HCF(992, 574, 470) = 2

HCF of 992, 574, 470 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 992, 574, 470 is 2.

Highest Common Factor of 992,574,470 using Euclid's algorithm

Highest Common Factor of 992,574,470 is 2

Step 1: Since 992 > 574, we apply the division lemma to 992 and 574, to get

992 = 574 x 1 + 418

Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 418 and 574, to get

574 = 418 x 1 + 156

Step 3: We consider the new divisor 418 and the new remainder 156, and apply the division lemma to get

418 = 156 x 2 + 106

We consider the new divisor 156 and the new remainder 106,and apply the division lemma to get

156 = 106 x 1 + 50

We consider the new divisor 106 and the new remainder 50,and apply the division lemma to get

106 = 50 x 2 + 6

We consider the new divisor 50 and the new remainder 6,and apply the division lemma to get

50 = 6 x 8 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 992 and 574 is 2

Notice that 2 = HCF(6,2) = HCF(50,6) = HCF(106,50) = HCF(156,106) = HCF(418,156) = HCF(574,418) = HCF(992,574) .

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

Step 1: Since 470 > 2, we apply the division lemma to 470 and 2, to get

470 = 2 x 235 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 470 is 2

Notice that 2 = HCF(470,2) .

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Frequently Asked Questions on HCF of 992, 574, 470 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 992, 574, 470?

Answer: HCF of 992, 574, 470 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 992, 574, 470 using Euclid's Algorithm?

Answer: For arbitrary numbers 992, 574, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.