Highest Common Factor of 658, 916, 265 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 658, 916, 265 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 658, 916, 265 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 658, 916, 265 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 658, 916, 265 is 1.

HCF(658, 916, 265) = 1

HCF of 658, 916, 265 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 658, 916, 265 is 1.

Highest Common Factor of 658,916,265 using Euclid's algorithm

Highest Common Factor of 658,916,265 is 1

Step 1: Since 916 > 658, we apply the division lemma to 916 and 658, to get

916 = 658 x 1 + 258

Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 258 and 658, to get

658 = 258 x 2 + 142

Step 3: We consider the new divisor 258 and the new remainder 142, and apply the division lemma to get

258 = 142 x 1 + 116

We consider the new divisor 142 and the new remainder 116,and apply the division lemma to get

142 = 116 x 1 + 26

We consider the new divisor 116 and the new remainder 26,and apply the division lemma to get

116 = 26 x 4 + 12

We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get

26 = 12 x 2 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 658 and 916 is 2

Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(116,26) = HCF(142,116) = HCF(258,142) = HCF(658,258) = HCF(916,658) .

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

Step 1: Since 265 > 2, we apply the division lemma to 265 and 2, to get

265 = 2 x 132 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 265 is 1

Notice that 1 = HCF(2,1) = HCF(265,2) .

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Frequently Asked Questions on HCF of 658, 916, 265 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 658, 916, 265?

Answer: HCF of 658, 916, 265 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 658, 916, 265 using Euclid's Algorithm?

Answer: For arbitrary numbers 658, 916, 265 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.