Highest Common Factor of 965, 370, 558 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 965, 370, 558 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 965, 370, 558 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 965, 370, 558 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 965, 370, 558 is 1.

HCF(965, 370, 558) = 1

HCF of 965, 370, 558 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 965, 370, 558 is 1.

Highest Common Factor of 965,370,558 using Euclid's algorithm

Highest Common Factor of 965,370,558 is 1

Step 1: Since 965 > 370, we apply the division lemma to 965 and 370, to get

965 = 370 x 2 + 225

Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 225 and 370, to get

370 = 225 x 1 + 145

Step 3: We consider the new divisor 225 and the new remainder 145, and apply the division lemma to get

225 = 145 x 1 + 80

We consider the new divisor 145 and the new remainder 80,and apply the division lemma to get

145 = 80 x 1 + 65

We consider the new divisor 80 and the new remainder 65,and apply the division lemma to get

80 = 65 x 1 + 15

We consider the new divisor 65 and the new remainder 15,and apply the division lemma to get

65 = 15 x 4 + 5

We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 965 and 370 is 5

Notice that 5 = HCF(15,5) = HCF(65,15) = HCF(80,65) = HCF(145,80) = HCF(225,145) = HCF(370,225) = HCF(965,370) .

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

Step 1: Since 558 > 5, we apply the division lemma to 558 and 5, to get

558 = 5 x 111 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 558 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(558,5) .

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Frequently Asked Questions on HCF of 965, 370, 558 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 965, 370, 558?

Answer: HCF of 965, 370, 558 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 965, 370, 558 using Euclid's Algorithm?

Answer: For arbitrary numbers 965, 370, 558 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.