Highest Common Factor of 921, 597, 416 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, 597, 416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 921, 597, 416 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, 597, 416 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, 597, 416 is 1.

HCF(921, 597, 416) = 1

HCF of 921, 597, 416 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, 597, 416 is 1.

Highest Common Factor of 921,597,416 using Euclid's algorithm

Highest Common Factor of 921,597,416 is 1

Step 1: Since 921 > 597, we apply the division lemma to 921 and 597, to get

921 = 597 x 1 + 324

Step 2: Since the reminder 597 ≠ 0, we apply division lemma to 324 and 597, to get

597 = 324 x 1 + 273

Step 3: We consider the new divisor 324 and the new remainder 273, and apply the division lemma to get

324 = 273 x 1 + 51

We consider the new divisor 273 and the new remainder 51,and apply the division lemma to get

273 = 51 x 5 + 18

We consider the new divisor 51 and the new remainder 18,and apply the division lemma to get

51 = 18 x 2 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 921 and 597 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(51,18) = HCF(273,51) = HCF(324,273) = HCF(597,324) = HCF(921,597) .

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

Step 1: Since 416 > 3, we apply the division lemma to 416 and 3, to get

416 = 3 x 138 + 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 416 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(416,3) .

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Frequently Asked Questions on HCF of 921, 597, 416 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, 597, 416?

Answer: HCF of 921, 597, 416 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 921, 597, 416 using Euclid's Algorithm?

Answer: For arbitrary numbers 921, 597, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.