Highest Common Factor of 977, 382, 209 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 977, 382, 209 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 977, 382, 209 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 977, 382, 209 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 977, 382, 209 is 1.

HCF(977, 382, 209) = 1

HCF of 977, 382, 209 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 977, 382, 209 is 1.

Highest Common Factor of 977,382,209 using Euclid's algorithm

Highest Common Factor of 977,382,209 is 1

Step 1: Since 977 > 382, we apply the division lemma to 977 and 382, to get

977 = 382 x 2 + 213

Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 213 and 382, to get

382 = 213 x 1 + 169

Step 3: We consider the new divisor 213 and the new remainder 169, and apply the division lemma to get

213 = 169 x 1 + 44

We consider the new divisor 169 and the new remainder 44,and apply the division lemma to get

169 = 44 x 3 + 37

We consider the new divisor 44 and the new remainder 37,and apply the division lemma to get

44 = 37 x 1 + 7

We consider the new divisor 37 and the new remainder 7,and apply the division lemma to get

37 = 7 x 5 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 977 and 382 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(37,7) = HCF(44,37) = HCF(169,44) = HCF(213,169) = HCF(382,213) = HCF(977,382) .

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

Step 1: Since 209 > 1, we apply the division lemma to 209 and 1, to get

209 = 1 x 209 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 209 is 1

Notice that 1 = HCF(209,1) .

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Frequently Asked Questions on HCF of 977, 382, 209 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 977, 382, 209?

Answer: HCF of 977, 382, 209 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 977, 382, 209 using Euclid's Algorithm?

Answer: For arbitrary numbers 977, 382, 209 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.