Highest Common Factor of 669, 866, 687, 553 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 669, 866, 687, 553 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 669, 866, 687, 553 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 669, 866, 687, 553 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 669, 866, 687, 553 is 1.

HCF(669, 866, 687, 553) = 1

HCF of 669, 866, 687, 553 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 669, 866, 687, 553 is 1.

Highest Common Factor of 669,866,687,553 using Euclid's algorithm

Highest Common Factor of 669,866,687,553 is 1

Step 1: Since 866 > 669, we apply the division lemma to 866 and 669, to get

866 = 669 x 1 + 197

Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 197 and 669, to get

669 = 197 x 3 + 78

Step 3: We consider the new divisor 197 and the new remainder 78, and apply the division lemma to get

197 = 78 x 2 + 41

We consider the new divisor 78 and the new remainder 41,and apply the division lemma to get

78 = 41 x 1 + 37

We consider the new divisor 41 and the new remainder 37,and apply the division lemma to get

41 = 37 x 1 + 4

We consider the new divisor 37 and the new remainder 4,and apply the division lemma to get

37 = 4 x 9 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 669 and 866 is 1

Notice that 1 = HCF(4,1) = HCF(37,4) = HCF(41,37) = HCF(78,41) = HCF(197,78) = HCF(669,197) = HCF(866,669) .

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

Step 1: Since 687 > 1, we apply the division lemma to 687 and 1, to get

687 = 1 x 687 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 687 is 1

Notice that 1 = HCF(687,1) .

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

Step 1: Since 553 > 1, we apply the division lemma to 553 and 1, to get

553 = 1 x 553 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 553 is 1

Notice that 1 = HCF(553,1) .

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Frequently Asked Questions on HCF of 669, 866, 687, 553 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 669, 866, 687, 553?

Answer: HCF of 669, 866, 687, 553 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 669, 866, 687, 553 using Euclid's Algorithm?

Answer: For arbitrary numbers 669, 866, 687, 553 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.