Highest Common Factor of 675, 406, 820, 969 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 675, 406, 820, 969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 406, 820, 969 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 675, 406, 820, 969 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 675, 406, 820, 969 is 1.

HCF(675, 406, 820, 969) = 1

HCF of 675, 406, 820, 969 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 675, 406, 820, 969 is 1.

Highest Common Factor of 675,406,820,969 using Euclid's algorithm

Highest Common Factor of 675,406,820,969 is 1

Step 1: Since 675 > 406, we apply the division lemma to 675 and 406, to get

675 = 406 x 1 + 269

Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 269 and 406, to get

406 = 269 x 1 + 137

Step 3: We consider the new divisor 269 and the new remainder 137, and apply the division lemma to get

269 = 137 x 1 + 132

We consider the new divisor 137 and the new remainder 132,and apply the division lemma to get

137 = 132 x 1 + 5

We consider the new divisor 132 and the new remainder 5,and apply the division lemma to get

132 = 5 x 26 + 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 675 and 406 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(132,5) = HCF(137,132) = HCF(269,137) = HCF(406,269) = HCF(675,406) .

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

Step 1: Since 820 > 1, we apply the division lemma to 820 and 1, to get

820 = 1 x 820 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 820 is 1

Notice that 1 = HCF(820,1) .

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

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

969 = 1 x 969 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 969 is 1

Notice that 1 = HCF(969,1) .

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Frequently Asked Questions on HCF of 675, 406, 820, 969 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 675, 406, 820, 969?

Answer: HCF of 675, 406, 820, 969 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 406, 820, 969 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 406, 820, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.