Highest Common Factor of 660, 750, 379 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 660, 750, 379 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 660, 750, 379 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 660, 750, 379 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 660, 750, 379 is 1.

HCF(660, 750, 379) = 1

HCF of 660, 750, 379 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 660, 750, 379 is 1.

Highest Common Factor of 660,750,379 using Euclid's algorithm

Highest Common Factor of 660,750,379 is 1

Step 1: Since 750 > 660, we apply the division lemma to 750 and 660, to get

750 = 660 x 1 + 90

Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 90 and 660, to get

660 = 90 x 7 + 30

Step 3: We consider the new divisor 90 and the new remainder 30, and apply the division lemma to get

90 = 30 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 660 and 750 is 30

Notice that 30 = HCF(90,30) = HCF(660,90) = HCF(750,660) .

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

Step 1: Since 379 > 30, we apply the division lemma to 379 and 30, to get

379 = 30 x 12 + 19

Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 19 and 30, to get

30 = 19 x 1 + 11

Step 3: We consider the new divisor 19 and the new remainder 11, and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 30 and 379 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(379,30) .

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Frequently Asked Questions on HCF of 660, 750, 379 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 660, 750, 379?

Answer: HCF of 660, 750, 379 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 660, 750, 379 using Euclid's Algorithm?

Answer: For arbitrary numbers 660, 750, 379 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.