Highest Common Factor of 960, 689, 556 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 960, 689, 556 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 960, 689, 556 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 960, 689, 556 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 960, 689, 556 is 1.

HCF(960, 689, 556) = 1

HCF of 960, 689, 556 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 960, 689, 556 is 1.

Highest Common Factor of 960,689,556 using Euclid's algorithm

Highest Common Factor of 960,689,556 is 1

Step 1: Since 960 > 689, we apply the division lemma to 960 and 689, to get

960 = 689 x 1 + 271

Step 2: Since the reminder 689 ≠ 0, we apply division lemma to 271 and 689, to get

689 = 271 x 2 + 147

Step 3: We consider the new divisor 271 and the new remainder 147, and apply the division lemma to get

271 = 147 x 1 + 124

We consider the new divisor 147 and the new remainder 124,and apply the division lemma to get

147 = 124 x 1 + 23

We consider the new divisor 124 and the new remainder 23,and apply the division lemma to get

124 = 23 x 5 + 9

We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get

23 = 9 x 2 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 960 and 689 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(124,23) = HCF(147,124) = HCF(271,147) = HCF(689,271) = HCF(960,689) .

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

Step 1: Since 556 > 1, we apply the division lemma to 556 and 1, to get

556 = 1 x 556 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 556 is 1

Notice that 1 = HCF(556,1) .

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Frequently Asked Questions on HCF of 960, 689, 556 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 960, 689, 556?

Answer: HCF of 960, 689, 556 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 960, 689, 556 using Euclid's Algorithm?

Answer: For arbitrary numbers 960, 689, 556 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.