Highest Common Factor of 500, 641, 666, 328 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 500, 641, 666, 328 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 500, 641, 666, 328 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 500, 641, 666, 328 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 500, 641, 666, 328 is 1.

HCF(500, 641, 666, 328) = 1

HCF of 500, 641, 666, 328 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 500, 641, 666, 328 is 1.

Highest Common Factor of 500,641,666,328 using Euclid's algorithm

Highest Common Factor of 500,641,666,328 is 1

Step 1: Since 641 > 500, we apply the division lemma to 641 and 500, to get

641 = 500 x 1 + 141

Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 141 and 500, to get

500 = 141 x 3 + 77

Step 3: We consider the new divisor 141 and the new remainder 77, and apply the division lemma to get

141 = 77 x 1 + 64

We consider the new divisor 77 and the new remainder 64,and apply the division lemma to get

77 = 64 x 1 + 13

We consider the new divisor 64 and the new remainder 13,and apply the division lemma to get

64 = 13 x 4 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 500 and 641 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(64,13) = HCF(77,64) = HCF(141,77) = HCF(500,141) = HCF(641,500) .

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

Step 1: Since 666 > 1, we apply the division lemma to 666 and 1, to get

666 = 1 x 666 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 666 is 1

Notice that 1 = HCF(666,1) .

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

Step 1: Since 328 > 1, we apply the division lemma to 328 and 1, to get

328 = 1 x 328 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 328 is 1

Notice that 1 = HCF(328,1) .

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Frequently Asked Questions on HCF of 500, 641, 666, 328 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 500, 641, 666, 328?

Answer: HCF of 500, 641, 666, 328 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 500, 641, 666, 328 using Euclid's Algorithm?

Answer: For arbitrary numbers 500, 641, 666, 328 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.