Highest Common Factor of 756, 484, 299 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 756, 484, 299 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 756, 484, 299 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 756, 484, 299 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 756, 484, 299 is 1.

HCF(756, 484, 299) = 1

HCF of 756, 484, 299 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 756, 484, 299 is 1.

Highest Common Factor of 756,484,299 using Euclid's algorithm

Highest Common Factor of 756,484,299 is 1

Step 1: Since 756 > 484, we apply the division lemma to 756 and 484, to get

756 = 484 x 1 + 272

Step 2: Since the reminder 484 ≠ 0, we apply division lemma to 272 and 484, to get

484 = 272 x 1 + 212

Step 3: We consider the new divisor 272 and the new remainder 212, and apply the division lemma to get

272 = 212 x 1 + 60

We consider the new divisor 212 and the new remainder 60,and apply the division lemma to get

212 = 60 x 3 + 32

We consider the new divisor 60 and the new remainder 32,and apply the division lemma to get

60 = 32 x 1 + 28

We consider the new divisor 32 and the new remainder 28,and apply the division lemma to get

32 = 28 x 1 + 4

We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get

28 = 4 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 756 and 484 is 4

Notice that 4 = HCF(28,4) = HCF(32,28) = HCF(60,32) = HCF(212,60) = HCF(272,212) = HCF(484,272) = HCF(756,484) .

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

Step 1: Since 299 > 4, we apply the division lemma to 299 and 4, to get

299 = 4 x 74 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 299 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(299,4) .

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Frequently Asked Questions on HCF of 756, 484, 299 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 756, 484, 299?

Answer: HCF of 756, 484, 299 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 756, 484, 299 using Euclid's Algorithm?

Answer: For arbitrary numbers 756, 484, 299 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.