Highest Common Factor of 7670, 1589 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 7670, 1589 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7670, 1589 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 7670, 1589 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 7670, 1589 is 1.

HCF(7670, 1589) = 1

HCF of 7670, 1589 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 7670, 1589 is 1.

Highest Common Factor of 7670,1589 using Euclid's algorithm

Highest Common Factor of 7670,1589 is 1

Step 1: Since 7670 > 1589, we apply the division lemma to 7670 and 1589, to get

7670 = 1589 x 4 + 1314

Step 2: Since the reminder 1589 ≠ 0, we apply division lemma to 1314 and 1589, to get

1589 = 1314 x 1 + 275

Step 3: We consider the new divisor 1314 and the new remainder 275, and apply the division lemma to get

1314 = 275 x 4 + 214

We consider the new divisor 275 and the new remainder 214,and apply the division lemma to get

275 = 214 x 1 + 61

We consider the new divisor 214 and the new remainder 61,and apply the division lemma to get

214 = 61 x 3 + 31

We consider the new divisor 61 and the new remainder 31,and apply the division lemma to get

61 = 31 x 1 + 30

We consider the new divisor 31 and the new remainder 30,and apply the division lemma to get

31 = 30 x 1 + 1

We consider the new divisor 30 and the new remainder 1,and apply the division lemma to get

30 = 1 x 30 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7670 and 1589 is 1

Notice that 1 = HCF(30,1) = HCF(31,30) = HCF(61,31) = HCF(214,61) = HCF(275,214) = HCF(1314,275) = HCF(1589,1314) = HCF(7670,1589) .

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Frequently Asked Questions on HCF of 7670, 1589 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 7670, 1589?

Answer: HCF of 7670, 1589 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7670, 1589 using Euclid's Algorithm?

Answer: For arbitrary numbers 7670, 1589 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.