Highest Common Factor of 300, 508, 746, 363 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 300, 508, 746, 363 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 300, 508, 746, 363 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 300, 508, 746, 363 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 300, 508, 746, 363 is 1.

HCF(300, 508, 746, 363) = 1

HCF of 300, 508, 746, 363 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 300, 508, 746, 363 is 1.

Highest Common Factor of 300,508,746,363 using Euclid's algorithm

Highest Common Factor of 300,508,746,363 is 1

Step 1: Since 508 > 300, we apply the division lemma to 508 and 300, to get

508 = 300 x 1 + 208

Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 208 and 300, to get

300 = 208 x 1 + 92

Step 3: We consider the new divisor 208 and the new remainder 92, and apply the division lemma to get

208 = 92 x 2 + 24

We consider the new divisor 92 and the new remainder 24,and apply the division lemma to get

92 = 24 x 3 + 20

We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get

24 = 20 x 1 + 4

We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 300 and 508 is 4

Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(92,24) = HCF(208,92) = HCF(300,208) = HCF(508,300) .

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

Step 1: Since 746 > 4, we apply the division lemma to 746 and 4, to get

746 = 4 x 186 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 746 is 2

Notice that 2 = HCF(4,2) = HCF(746,4) .

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

Step 1: Since 363 > 2, we apply the division lemma to 363 and 2, to get

363 = 2 x 181 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 363 is 1

Notice that 1 = HCF(2,1) = HCF(363,2) .

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Frequently Asked Questions on HCF of 300, 508, 746, 363 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 300, 508, 746, 363?

Answer: HCF of 300, 508, 746, 363 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 300, 508, 746, 363 using Euclid's Algorithm?

Answer: For arbitrary numbers 300, 508, 746, 363 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.