Highest Common Factor of 675, 803, 77 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 675, 803, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 803, 77 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 675, 803, 77 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 675, 803, 77 is 1.

HCF(675, 803, 77) = 1

HCF of 675, 803, 77 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 675, 803, 77 is 1.

Highest Common Factor of 675,803,77 using Euclid's algorithm

Highest Common Factor of 675,803,77 is 1

Step 1: Since 803 > 675, we apply the division lemma to 803 and 675, to get

803 = 675 x 1 + 128

Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 128 and 675, to get

675 = 128 x 5 + 35

Step 3: We consider the new divisor 128 and the new remainder 35, and apply the division lemma to get

128 = 35 x 3 + 23

We consider the new divisor 35 and the new remainder 23,and apply the division lemma to get

35 = 23 x 1 + 12

We consider the new divisor 23 and the new remainder 12,and apply the division lemma to get

23 = 12 x 1 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 675 and 803 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(23,12) = HCF(35,23) = HCF(128,35) = HCF(675,128) = HCF(803,675) .

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

Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get

77 = 1 x 77 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1

Notice that 1 = HCF(77,1) .

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Frequently Asked Questions on HCF of 675, 803, 77 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 675, 803, 77?

Answer: HCF of 675, 803, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 803, 77 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 803, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.