Highest Common Factor of 688, 273, 161 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, 273, 161 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 688, 273, 161 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, 273, 161 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, 273, 161 is 1.

HCF(688, 273, 161) = 1

HCF of 688, 273, 161 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, 273, 161 is 1.

Highest Common Factor of 688,273,161 using Euclid's algorithm

Highest Common Factor of 688,273,161 is 1

Step 1: Since 688 > 273, we apply the division lemma to 688 and 273, to get

688 = 273 x 2 + 142

Step 2: Since the reminder 273 ≠ 0, we apply division lemma to 142 and 273, to get

273 = 142 x 1 + 131

Step 3: We consider the new divisor 142 and the new remainder 131, and apply the division lemma to get

142 = 131 x 1 + 11

We consider the new divisor 131 and the new remainder 11,and apply the division lemma to get

131 = 11 x 11 + 10

We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get

11 = 10 x 1 + 1

We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 688 and 273 is 1

Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(131,11) = HCF(142,131) = HCF(273,142) = HCF(688,273) .

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

Step 1: Since 161 > 1, we apply the division lemma to 161 and 1, to get

161 = 1 x 161 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 161 is 1

Notice that 1 = HCF(161,1) .

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Frequently Asked Questions on HCF of 688, 273, 161 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, 273, 161?

Answer: HCF of 688, 273, 161 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 688, 273, 161 using Euclid's Algorithm?

Answer: For arbitrary numbers 688, 273, 161 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.