Highest Common Factor of 497, 688, 105 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 497, 688, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 497, 688, 105 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 497, 688, 105 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 497, 688, 105 is 1.

HCF(497, 688, 105) = 1

HCF of 497, 688, 105 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 497, 688, 105 is 1.

Highest Common Factor of 497,688,105 using Euclid's algorithm

Highest Common Factor of 497,688,105 is 1

Step 1: Since 688 > 497, we apply the division lemma to 688 and 497, to get

688 = 497 x 1 + 191

Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 191 and 497, to get

497 = 191 x 2 + 115

Step 3: We consider the new divisor 191 and the new remainder 115, and apply the division lemma to get

191 = 115 x 1 + 76

We consider the new divisor 115 and the new remainder 76,and apply the division lemma to get

115 = 76 x 1 + 39

We consider the new divisor 76 and the new remainder 39,and apply the division lemma to get

76 = 39 x 1 + 37

We consider the new divisor 39 and the new remainder 37,and apply the division lemma to get

39 = 37 x 1 + 2

We consider the new divisor 37 and the new remainder 2,and apply the division lemma to get

37 = 2 x 18 + 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 497 and 688 is 1

Notice that 1 = HCF(2,1) = HCF(37,2) = HCF(39,37) = HCF(76,39) = HCF(115,76) = HCF(191,115) = HCF(497,191) = HCF(688,497) .

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

Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get

105 = 1 x 105 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1

Notice that 1 = HCF(105,1) .

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Frequently Asked Questions on HCF of 497, 688, 105 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 497, 688, 105?

Answer: HCF of 497, 688, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 497, 688, 105 using Euclid's Algorithm?

Answer: For arbitrary numbers 497, 688, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.