Highest Common Factor of 759, 672, 822, 28 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 759, 672, 822, 28 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 759, 672, 822, 28 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 759, 672, 822, 28 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 759, 672, 822, 28 is 1.

HCF(759, 672, 822, 28) = 1

HCF of 759, 672, 822, 28 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 759, 672, 822, 28 is 1.

Highest Common Factor of 759,672,822,28 using Euclid's algorithm

Highest Common Factor of 759,672,822,28 is 1

Step 1: Since 759 > 672, we apply the division lemma to 759 and 672, to get

759 = 672 x 1 + 87

Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 87 and 672, to get

672 = 87 x 7 + 63

Step 3: We consider the new divisor 87 and the new remainder 63, and apply the division lemma to get

87 = 63 x 1 + 24

We consider the new divisor 63 and the new remainder 24,and apply the division lemma to get

63 = 24 x 2 + 15

We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get

24 = 15 x 1 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 759 and 672 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(63,24) = HCF(87,63) = HCF(672,87) = HCF(759,672) .

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

Step 1: Since 822 > 3, we apply the division lemma to 822 and 3, to get

822 = 3 x 274 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 822 is 3

Notice that 3 = HCF(822,3) .

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

Step 1: Since 28 > 3, we apply the division lemma to 28 and 3, to get

28 = 3 x 9 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 28 is 1

Notice that 1 = HCF(3,1) = HCF(28,3) .

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Frequently Asked Questions on HCF of 759, 672, 822, 28 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 759, 672, 822, 28?

Answer: HCF of 759, 672, 822, 28 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 759, 672, 822, 28 using Euclid's Algorithm?

Answer: For arbitrary numbers 759, 672, 822, 28 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.