Highest Common Factor of 669, 985, 515 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, 985, 515 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 669, 985, 515 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, 985, 515 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, 985, 515 is 1.

HCF(669, 985, 515) = 1

HCF of 669, 985, 515 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, 985, 515 is 1.

Highest Common Factor of 669,985,515 using Euclid's algorithm

Highest Common Factor of 669,985,515 is 1

Step 1: Since 985 > 669, we apply the division lemma to 985 and 669, to get

985 = 669 x 1 + 316

Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 316 and 669, to get

669 = 316 x 2 + 37

Step 3: We consider the new divisor 316 and the new remainder 37, and apply the division lemma to get

316 = 37 x 8 + 20

We consider the new divisor 37 and the new remainder 20,and apply the division lemma to get

37 = 20 x 1 + 17

We consider the new divisor 20 and the new remainder 17,and apply the division lemma to get

20 = 17 x 1 + 3

We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get

17 = 3 x 5 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 669 and 985 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(20,17) = HCF(37,20) = HCF(316,37) = HCF(669,316) = HCF(985,669) .

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

Step 1: Since 515 > 1, we apply the division lemma to 515 and 1, to get

515 = 1 x 515 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 515 is 1

Notice that 1 = HCF(515,1) .

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Frequently Asked Questions on HCF of 669, 985, 515 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, 985, 515?

Answer: HCF of 669, 985, 515 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 669, 985, 515 using Euclid's Algorithm?

Answer: For arbitrary numbers 669, 985, 515 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.