Highest Common Factor of 689, 570, 305 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 689, 570, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 689, 570, 305 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 689, 570, 305 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 689, 570, 305 is 1.

HCF(689, 570, 305) = 1

HCF of 689, 570, 305 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 689, 570, 305 is 1.

Highest Common Factor of 689,570,305 using Euclid's algorithm

Highest Common Factor of 689,570,305 is 1

Step 1: Since 689 > 570, we apply the division lemma to 689 and 570, to get

689 = 570 x 1 + 119

Step 2: Since the reminder 570 ≠ 0, we apply division lemma to 119 and 570, to get

570 = 119 x 4 + 94

Step 3: We consider the new divisor 119 and the new remainder 94, and apply the division lemma to get

119 = 94 x 1 + 25

We consider the new divisor 94 and the new remainder 25,and apply the division lemma to get

94 = 25 x 3 + 19

We consider the new divisor 25 and the new remainder 19,and apply the division lemma to get

25 = 19 x 1 + 6

We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get

19 = 6 x 3 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 689 and 570 is 1

Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(25,19) = HCF(94,25) = HCF(119,94) = HCF(570,119) = HCF(689,570) .

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

Step 1: Since 305 > 1, we apply the division lemma to 305 and 1, to get

305 = 1 x 305 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 305 is 1

Notice that 1 = HCF(305,1) .

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Frequently Asked Questions on HCF of 689, 570, 305 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 689, 570, 305?

Answer: HCF of 689, 570, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 689, 570, 305 using Euclid's Algorithm?

Answer: For arbitrary numbers 689, 570, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.