Highest Common Factor of 334, 852, 992 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 334, 852, 992 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 334, 852, 992 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 334, 852, 992 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 334, 852, 992 is 2.

HCF(334, 852, 992) = 2

HCF of 334, 852, 992 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 334, 852, 992 is 2.

Highest Common Factor of 334,852,992 using Euclid's algorithm

Highest Common Factor of 334,852,992 is 2

Step 1: Since 852 > 334, we apply the division lemma to 852 and 334, to get

852 = 334 x 2 + 184

Step 2: Since the reminder 334 ≠ 0, we apply division lemma to 184 and 334, to get

334 = 184 x 1 + 150

Step 3: We consider the new divisor 184 and the new remainder 150, and apply the division lemma to get

184 = 150 x 1 + 34

We consider the new divisor 150 and the new remainder 34,and apply the division lemma to get

150 = 34 x 4 + 14

We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get

34 = 14 x 2 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 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 334 and 852 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(150,34) = HCF(184,150) = HCF(334,184) = HCF(852,334) .

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

Step 1: Since 992 > 2, we apply the division lemma to 992 and 2, to get

992 = 2 x 496 + 0

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

Notice that 2 = HCF(992,2) .

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Frequently Asked Questions on HCF of 334, 852, 992 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 334, 852, 992?

Answer: HCF of 334, 852, 992 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 334, 852, 992 using Euclid's Algorithm?

Answer: For arbitrary numbers 334, 852, 992 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.