Highest Common Factor of 921, 554, 18 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 921, 554, 18 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 921, 554, 18 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 921, 554, 18 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 921, 554, 18 is 1.

HCF(921, 554, 18) = 1

HCF of 921, 554, 18 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 921, 554, 18 is 1.

Highest Common Factor of 921,554,18 using Euclid's algorithm

Highest Common Factor of 921,554,18 is 1

Step 1: Since 921 > 554, we apply the division lemma to 921 and 554, to get

921 = 554 x 1 + 367

Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 367 and 554, to get

554 = 367 x 1 + 187

Step 3: We consider the new divisor 367 and the new remainder 187, and apply the division lemma to get

367 = 187 x 1 + 180

We consider the new divisor 187 and the new remainder 180,and apply the division lemma to get

187 = 180 x 1 + 7

We consider the new divisor 180 and the new remainder 7,and apply the division lemma to get

180 = 7 x 25 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 921 and 554 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(180,7) = HCF(187,180) = HCF(367,187) = HCF(554,367) = HCF(921,554) .

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

Step 1: Since 18 > 1, we apply the division lemma to 18 and 1, to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 18 is 1

Notice that 1 = HCF(18,1) .

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Frequently Asked Questions on HCF of 921, 554, 18 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 921, 554, 18?

Answer: HCF of 921, 554, 18 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 921, 554, 18 using Euclid's Algorithm?

Answer: For arbitrary numbers 921, 554, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.