Highest Common Factor of 377, 986, 393, 75 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 377, 986, 393, 75 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 377, 986, 393, 75 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 377, 986, 393, 75 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 377, 986, 393, 75 is 1.

HCF(377, 986, 393, 75) = 1

HCF of 377, 986, 393, 75 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 377, 986, 393, 75 is 1.

Highest Common Factor of 377,986,393,75 using Euclid's algorithm

Highest Common Factor of 377,986,393,75 is 1

Step 1: Since 986 > 377, we apply the division lemma to 986 and 377, to get

986 = 377 x 2 + 232

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 232 and 377, to get

377 = 232 x 1 + 145

Step 3: We consider the new divisor 232 and the new remainder 145, and apply the division lemma to get

232 = 145 x 1 + 87

We consider the new divisor 145 and the new remainder 87,and apply the division lemma to get

145 = 87 x 1 + 58

We consider the new divisor 87 and the new remainder 58,and apply the division lemma to get

87 = 58 x 1 + 29

We consider the new divisor 58 and the new remainder 29,and apply the division lemma to get

58 = 29 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 29, the HCF of 377 and 986 is 29

Notice that 29 = HCF(58,29) = HCF(87,58) = HCF(145,87) = HCF(232,145) = HCF(377,232) = HCF(986,377) .

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

Step 1: Since 393 > 29, we apply the division lemma to 393 and 29, to get

393 = 29 x 13 + 16

Step 2: Since the reminder 29 ≠ 0, we apply division lemma to 16 and 29, to get

29 = 16 x 1 + 13

Step 3: We consider the new divisor 16 and the new remainder 13, and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

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 29 and 393 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(393,29) .

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

Step 1: Since 75 > 1, we apply the division lemma to 75 and 1, to get

75 = 1 x 75 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 75 is 1

Notice that 1 = HCF(75,1) .

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Frequently Asked Questions on HCF of 377, 986, 393, 75 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 377, 986, 393, 75?

Answer: HCF of 377, 986, 393, 75 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 377, 986, 393, 75 using Euclid's Algorithm?

Answer: For arbitrary numbers 377, 986, 393, 75 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.