Highest Common Factor of 669, 437, 689 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, 437, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 669, 437, 689 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, 437, 689 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, 437, 689 is 1.

HCF(669, 437, 689) = 1

HCF of 669, 437, 689 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, 437, 689 is 1.

Highest Common Factor of 669,437,689 using Euclid's algorithm

Highest Common Factor of 669,437,689 is 1

Step 1: Since 669 > 437, we apply the division lemma to 669 and 437, to get

669 = 437 x 1 + 232

Step 2: Since the reminder 437 ≠ 0, we apply division lemma to 232 and 437, to get

437 = 232 x 1 + 205

Step 3: We consider the new divisor 232 and the new remainder 205, and apply the division lemma to get

232 = 205 x 1 + 27

We consider the new divisor 205 and the new remainder 27,and apply the division lemma to get

205 = 27 x 7 + 16

We consider the new divisor 27 and the new remainder 16,and apply the division lemma to get

27 = 16 x 1 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 669 and 437 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(27,16) = HCF(205,27) = HCF(232,205) = HCF(437,232) = HCF(669,437) .

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

Step 1: Since 689 > 1, we apply the division lemma to 689 and 1, to get

689 = 1 x 689 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 689 is 1

Notice that 1 = HCF(689,1) .

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Frequently Asked Questions on HCF of 669, 437, 689 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, 437, 689?

Answer: HCF of 669, 437, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 669, 437, 689 using Euclid's Algorithm?

Answer: For arbitrary numbers 669, 437, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.