Highest Common Factor of 688, 445, 217 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 688, 445, 217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 688, 445, 217 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 688, 445, 217 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 688, 445, 217 is 1.

HCF(688, 445, 217) = 1

HCF of 688, 445, 217 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 688, 445, 217 is 1.

Highest Common Factor of 688,445,217 using Euclid's algorithm

Highest Common Factor of 688,445,217 is 1

Step 1: Since 688 > 445, we apply the division lemma to 688 and 445, to get

688 = 445 x 1 + 243

Step 2: Since the reminder 445 ≠ 0, we apply division lemma to 243 and 445, to get

445 = 243 x 1 + 202

Step 3: We consider the new divisor 243 and the new remainder 202, and apply the division lemma to get

243 = 202 x 1 + 41

We consider the new divisor 202 and the new remainder 41,and apply the division lemma to get

202 = 41 x 4 + 38

We consider the new divisor 41 and the new remainder 38,and apply the division lemma to get

41 = 38 x 1 + 3

We consider the new divisor 38 and the new remainder 3,and apply the division lemma to get

38 = 3 x 12 + 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 688 and 445 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(38,3) = HCF(41,38) = HCF(202,41) = HCF(243,202) = HCF(445,243) = HCF(688,445) .

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

Step 1: Since 217 > 1, we apply the division lemma to 217 and 1, to get

217 = 1 x 217 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 217 is 1

Notice that 1 = HCF(217,1) .

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Frequently Asked Questions on HCF of 688, 445, 217 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 688, 445, 217?

Answer: HCF of 688, 445, 217 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 688, 445, 217 using Euclid's Algorithm?

Answer: For arbitrary numbers 688, 445, 217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.