Highest Common Factor of 969, 589, 306, 559 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 969, 589, 306, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 969, 589, 306, 559 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 969, 589, 306, 559 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 969, 589, 306, 559 is 1.

HCF(969, 589, 306, 559) = 1

HCF of 969, 589, 306, 559 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 969, 589, 306, 559 is 1.

Highest Common Factor of 969,589,306,559 using Euclid's algorithm

Highest Common Factor of 969,589,306,559 is 1

Step 1: Since 969 > 589, we apply the division lemma to 969 and 589, to get

969 = 589 x 1 + 380

Step 2: Since the reminder 589 ≠ 0, we apply division lemma to 380 and 589, to get

589 = 380 x 1 + 209

Step 3: We consider the new divisor 380 and the new remainder 209, and apply the division lemma to get

380 = 209 x 1 + 171

We consider the new divisor 209 and the new remainder 171,and apply the division lemma to get

209 = 171 x 1 + 38

We consider the new divisor 171 and the new remainder 38,and apply the division lemma to get

171 = 38 x 4 + 19

We consider the new divisor 38 and the new remainder 19,and apply the division lemma to get

38 = 19 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 969 and 589 is 19

Notice that 19 = HCF(38,19) = HCF(171,38) = HCF(209,171) = HCF(380,209) = HCF(589,380) = HCF(969,589) .

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

Step 1: Since 306 > 19, we apply the division lemma to 306 and 19, to get

306 = 19 x 16 + 2

Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 2 and 19, to get

19 = 2 x 9 + 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 19 and 306 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(306,19) .

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

Step 1: Since 559 > 1, we apply the division lemma to 559 and 1, to get

559 = 1 x 559 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 559 is 1

Notice that 1 = HCF(559,1) .

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Frequently Asked Questions on HCF of 969, 589, 306, 559 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 969, 589, 306, 559?

Answer: HCF of 969, 589, 306, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 969, 589, 306, 559 using Euclid's Algorithm?

Answer: For arbitrary numbers 969, 589, 306, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.