Highest Common Factor of 748, 7016, 6359 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 748, 7016, 6359 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 748, 7016, 6359 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 748, 7016, 6359 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 748, 7016, 6359 is 1.

HCF(748, 7016, 6359) = 1

HCF of 748, 7016, 6359 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 748, 7016, 6359 is 1.

Highest Common Factor of 748,7016,6359 using Euclid's algorithm

Highest Common Factor of 748,7016,6359 is 1

Step 1: Since 7016 > 748, we apply the division lemma to 7016 and 748, to get

7016 = 748 x 9 + 284

Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 284 and 748, to get

748 = 284 x 2 + 180

Step 3: We consider the new divisor 284 and the new remainder 180, and apply the division lemma to get

284 = 180 x 1 + 104

We consider the new divisor 180 and the new remainder 104,and apply the division lemma to get

180 = 104 x 1 + 76

We consider the new divisor 104 and the new remainder 76,and apply the division lemma to get

104 = 76 x 1 + 28

We consider the new divisor 76 and the new remainder 28,and apply the division lemma to get

76 = 28 x 2 + 20

We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get

28 = 20 x 1 + 8

We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get

20 = 8 x 2 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 748 and 7016 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(76,28) = HCF(104,76) = HCF(180,104) = HCF(284,180) = HCF(748,284) = HCF(7016,748) .

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

Step 1: Since 6359 > 4, we apply the division lemma to 6359 and 4, to get

6359 = 4 x 1589 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 6359 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(6359,4) .

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Frequently Asked Questions on HCF of 748, 7016, 6359 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 748, 7016, 6359?

Answer: HCF of 748, 7016, 6359 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 748, 7016, 6359 using Euclid's Algorithm?

Answer: For arbitrary numbers 748, 7016, 6359 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.