Highest Common Factor of 7784, 1588, 83969 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 7784, 1588, 83969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7784, 1588, 83969 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 7784, 1588, 83969 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 7784, 1588, 83969 is 1.

HCF(7784, 1588, 83969) = 1

HCF of 7784, 1588, 83969 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 7784, 1588, 83969 is 1.

Highest Common Factor of 7784,1588,83969 using Euclid's algorithm

Highest Common Factor of 7784,1588,83969 is 1

Step 1: Since 7784 > 1588, we apply the division lemma to 7784 and 1588, to get

7784 = 1588 x 4 + 1432

Step 2: Since the reminder 1588 ≠ 0, we apply division lemma to 1432 and 1588, to get

1588 = 1432 x 1 + 156

Step 3: We consider the new divisor 1432 and the new remainder 156, and apply the division lemma to get

1432 = 156 x 9 + 28

We consider the new divisor 156 and the new remainder 28,and apply the division lemma to get

156 = 28 x 5 + 16

We consider the new divisor 28 and the new remainder 16,and apply the division lemma to get

28 = 16 x 1 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 7784 and 1588 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(28,16) = HCF(156,28) = HCF(1432,156) = HCF(1588,1432) = HCF(7784,1588) .

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

Step 1: Since 83969 > 4, we apply the division lemma to 83969 and 4, to get

83969 = 4 x 20992 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 83969 is 1

Notice that 1 = HCF(4,1) = HCF(83969,4) .

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Frequently Asked Questions on HCF of 7784, 1588, 83969 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 7784, 1588, 83969?

Answer: HCF of 7784, 1588, 83969 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7784, 1588, 83969 using Euclid's Algorithm?

Answer: For arbitrary numbers 7784, 1588, 83969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.