Highest Common Factor of 5973, 7649 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 5973, 7649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5973, 7649 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 5973, 7649 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 5973, 7649 is 1.

HCF(5973, 7649) = 1

HCF of 5973, 7649 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 5973, 7649 is 1.

Highest Common Factor of 5973,7649 using Euclid's algorithm

Highest Common Factor of 5973,7649 is 1

Step 1: Since 7649 > 5973, we apply the division lemma to 7649 and 5973, to get

7649 = 5973 x 1 + 1676

Step 2: Since the reminder 5973 ≠ 0, we apply division lemma to 1676 and 5973, to get

5973 = 1676 x 3 + 945

Step 3: We consider the new divisor 1676 and the new remainder 945, and apply the division lemma to get

1676 = 945 x 1 + 731

We consider the new divisor 945 and the new remainder 731,and apply the division lemma to get

945 = 731 x 1 + 214

We consider the new divisor 731 and the new remainder 214,and apply the division lemma to get

731 = 214 x 3 + 89

We consider the new divisor 214 and the new remainder 89,and apply the division lemma to get

214 = 89 x 2 + 36

We consider the new divisor 89 and the new remainder 36,and apply the division lemma to get

89 = 36 x 2 + 17

We consider the new divisor 36 and the new remainder 17,and apply the division lemma to get

36 = 17 x 2 + 2

We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get

17 = 2 x 8 + 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 5973 and 7649 is 1

Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(36,17) = HCF(89,36) = HCF(214,89) = HCF(731,214) = HCF(945,731) = HCF(1676,945) = HCF(5973,1676) = HCF(7649,5973) .

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Frequently Asked Questions on HCF of 5973, 7649 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 5973, 7649?

Answer: HCF of 5973, 7649 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5973, 7649 using Euclid's Algorithm?

Answer: For arbitrary numbers 5973, 7649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.