Highest Common Factor of 905, 658, 908 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 905, 658, 908 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 905, 658, 908 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 905, 658, 908 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 905, 658, 908 is 1.

HCF(905, 658, 908) = 1

HCF of 905, 658, 908 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 905, 658, 908 is 1.

Highest Common Factor of 905,658,908 using Euclid's algorithm

Highest Common Factor of 905,658,908 is 1

Step 1: Since 905 > 658, we apply the division lemma to 905 and 658, to get

905 = 658 x 1 + 247

Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 247 and 658, to get

658 = 247 x 2 + 164

Step 3: We consider the new divisor 247 and the new remainder 164, and apply the division lemma to get

247 = 164 x 1 + 83

We consider the new divisor 164 and the new remainder 83,and apply the division lemma to get

164 = 83 x 1 + 81

We consider the new divisor 83 and the new remainder 81,and apply the division lemma to get

83 = 81 x 1 + 2

We consider the new divisor 81 and the new remainder 2,and apply the division lemma to get

81 = 2 x 40 + 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 905 and 658 is 1

Notice that 1 = HCF(2,1) = HCF(81,2) = HCF(83,81) = HCF(164,83) = HCF(247,164) = HCF(658,247) = HCF(905,658) .

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

Step 1: Since 908 > 1, we apply the division lemma to 908 and 1, to get

908 = 1 x 908 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 908 is 1

Notice that 1 = HCF(908,1) .

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Frequently Asked Questions on HCF of 905, 658, 908 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 905, 658, 908?

Answer: HCF of 905, 658, 908 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 905, 658, 908 using Euclid's Algorithm?

Answer: For arbitrary numbers 905, 658, 908 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.