Highest Common Factor of 993, 624, 113 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 993, 624, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 993, 624, 113 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 993, 624, 113 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 993, 624, 113 is 1.

HCF(993, 624, 113) = 1

HCF of 993, 624, 113 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 993, 624, 113 is 1.

Highest Common Factor of 993,624,113 using Euclid's algorithm

Highest Common Factor of 993,624,113 is 1

Step 1: Since 993 > 624, we apply the division lemma to 993 and 624, to get

993 = 624 x 1 + 369

Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 369 and 624, to get

624 = 369 x 1 + 255

Step 3: We consider the new divisor 369 and the new remainder 255, and apply the division lemma to get

369 = 255 x 1 + 114

We consider the new divisor 255 and the new remainder 114,and apply the division lemma to get

255 = 114 x 2 + 27

We consider the new divisor 114 and the new remainder 27,and apply the division lemma to get

114 = 27 x 4 + 6

We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get

27 = 6 x 4 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 993 and 624 is 3

Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(114,27) = HCF(255,114) = HCF(369,255) = HCF(624,369) = HCF(993,624) .

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

Step 1: Since 113 > 3, we apply the division lemma to 113 and 3, to get

113 = 3 x 37 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 113 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(113,3) .

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Frequently Asked Questions on HCF of 993, 624, 113 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 993, 624, 113?

Answer: HCF of 993, 624, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 993, 624, 113 using Euclid's Algorithm?

Answer: For arbitrary numbers 993, 624, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.