Highest Common Factor of 364, 280, 993 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 364, 280, 993 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 364, 280, 993 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 364, 280, 993 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 364, 280, 993 is 1.

HCF(364, 280, 993) = 1

HCF of 364, 280, 993 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 364, 280, 993 is 1.

Highest Common Factor of 364,280,993 using Euclid's algorithm

Highest Common Factor of 364,280,993 is 1

Step 1: Since 364 > 280, we apply the division lemma to 364 and 280, to get

364 = 280 x 1 + 84

Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 84 and 280, to get

280 = 84 x 3 + 28

Step 3: We consider the new divisor 84 and the new remainder 28, and apply the division lemma to get

84 = 28 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 28, the HCF of 364 and 280 is 28

Notice that 28 = HCF(84,28) = HCF(280,84) = HCF(364,280) .

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

Step 1: Since 993 > 28, we apply the division lemma to 993 and 28, to get

993 = 28 x 35 + 13

Step 2: Since the reminder 28 ≠ 0, we apply division lemma to 13 and 28, to get

28 = 13 x 2 + 2

Step 3: We consider the new divisor 13 and the new remainder 2, and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 28 and 993 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(28,13) = HCF(993,28) .

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Frequently Asked Questions on HCF of 364, 280, 993 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 364, 280, 993?

Answer: HCF of 364, 280, 993 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 364, 280, 993 using Euclid's Algorithm?

Answer: For arbitrary numbers 364, 280, 993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.