Highest Common Factor of 387, 603, 855, 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 387, 603, 855, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 387, 603, 855, 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 387, 603, 855, 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 387, 603, 855, 77 is 1.

HCF(387, 603, 855, 77) = 1

HCF of 387, 603, 855, 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 387, 603, 855, 77 is 1.

Highest Common Factor of 387,603,855,77 using Euclid's algorithm

Highest Common Factor of 387,603,855,77 is 1

Step 1: Since 603 > 387, we apply the division lemma to 603 and 387, to get

603 = 387 x 1 + 216

Step 2: Since the reminder 387 ≠ 0, we apply division lemma to 216 and 387, to get

387 = 216 x 1 + 171

Step 3: We consider the new divisor 216 and the new remainder 171, and apply the division lemma to get

216 = 171 x 1 + 45

We consider the new divisor 171 and the new remainder 45,and apply the division lemma to get

171 = 45 x 3 + 36

We consider the new divisor 45 and the new remainder 36,and apply the division lemma to get

45 = 36 x 1 + 9

We consider the new divisor 36 and the new remainder 9,and apply the division lemma to get

36 = 9 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 387 and 603 is 9

Notice that 9 = HCF(36,9) = HCF(45,36) = HCF(171,45) = HCF(216,171) = HCF(387,216) = HCF(603,387) .

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

Step 1: Since 855 > 9, we apply the division lemma to 855 and 9, to get

855 = 9 x 95 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 855 is 9

Notice that 9 = HCF(855,9) .

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

Step 1: Since 77 > 9, we apply the division lemma to 77 and 9, to get

77 = 9 x 8 + 5

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 5 and 9, to get

9 = 5 x 1 + 4

Step 3: We consider the new divisor 5 and the new remainder 4, and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1, and apply the division lemma 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 9 and 77 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(77,9) .

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Frequently Asked Questions on HCF of 387, 603, 855, 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 387, 603, 855, 77?

Answer: HCF of 387, 603, 855, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 387, 603, 855, 77 using Euclid's Algorithm?

Answer: For arbitrary numbers 387, 603, 855, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.