Highest Common Factor of 414, 682, 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 414, 682, 993 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 414, 682, 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 414, 682, 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 414, 682, 993 is 1.

HCF(414, 682, 993) = 1

HCF of 414, 682, 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 414, 682, 993 is 1.

Highest Common Factor of 414,682,993 using Euclid's algorithm

Highest Common Factor of 414,682,993 is 1

Step 1: Since 682 > 414, we apply the division lemma to 682 and 414, to get

682 = 414 x 1 + 268

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 268 and 414, to get

414 = 268 x 1 + 146

Step 3: We consider the new divisor 268 and the new remainder 146, and apply the division lemma to get

268 = 146 x 1 + 122

We consider the new divisor 146 and the new remainder 122,and apply the division lemma to get

146 = 122 x 1 + 24

We consider the new divisor 122 and the new remainder 24,and apply the division lemma to get

122 = 24 x 5 + 2

We consider the new divisor 24 and the new remainder 2,and apply the division lemma to get

24 = 2 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 414 and 682 is 2

Notice that 2 = HCF(24,2) = HCF(122,24) = HCF(146,122) = HCF(268,146) = HCF(414,268) = HCF(682,414) .

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

Step 1: Since 993 > 2, we apply the division lemma to 993 and 2, to get

993 = 2 x 496 + 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 993 is 1

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

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Frequently Asked Questions on HCF of 414, 682, 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 414, 682, 993?

Answer: HCF of 414, 682, 993 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 414, 682, 993 using Euclid's Algorithm?

Answer: For arbitrary numbers 414, 682, 993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.