Highest Common Factor of 992, 392, 378 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, 392, 378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 992, 392, 378 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, 392, 378 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, 392, 378 is 2.

HCF(992, 392, 378) = 2

HCF of 992, 392, 378 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, 392, 378 is 2.

Highest Common Factor of 992,392,378 using Euclid's algorithm

Highest Common Factor of 992,392,378 is 2

Step 1: Since 992 > 392, we apply the division lemma to 992 and 392, to get

992 = 392 x 2 + 208

Step 2: Since the reminder 392 ≠ 0, we apply division lemma to 208 and 392, to get

392 = 208 x 1 + 184

Step 3: We consider the new divisor 208 and the new remainder 184, and apply the division lemma to get

208 = 184 x 1 + 24

We consider the new divisor 184 and the new remainder 24,and apply the division lemma to get

184 = 24 x 7 + 16

We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get

24 = 16 x 1 + 8

We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 992 and 392 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(184,24) = HCF(208,184) = HCF(392,208) = HCF(992,392) .

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

Step 1: Since 378 > 8, we apply the division lemma to 378 and 8, to get

378 = 8 x 47 + 2

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 378 is 2

Notice that 2 = HCF(8,2) = HCF(378,8) .

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Frequently Asked Questions on HCF of 992, 392, 378 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, 392, 378?

Answer: HCF of 992, 392, 378 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 992, 392, 378 using Euclid's Algorithm?

Answer: For arbitrary numbers 992, 392, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.