Highest Common Factor of 299, 782, 372 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 299, 782, 372 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 299, 782, 372 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 299, 782, 372 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 299, 782, 372 is 1.

HCF(299, 782, 372) = 1

HCF of 299, 782, 372 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 299, 782, 372 is 1.

Highest Common Factor of 299,782,372 using Euclid's algorithm

Highest Common Factor of 299,782,372 is 1

Step 1: Since 782 > 299, we apply the division lemma to 782 and 299, to get

782 = 299 x 2 + 184

Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 184 and 299, to get

299 = 184 x 1 + 115

Step 3: We consider the new divisor 184 and the new remainder 115, and apply the division lemma to get

184 = 115 x 1 + 69

We consider the new divisor 115 and the new remainder 69,and apply the division lemma to get

115 = 69 x 1 + 46

We consider the new divisor 69 and the new remainder 46,and apply the division lemma to get

69 = 46 x 1 + 23

We consider the new divisor 46 and the new remainder 23,and apply the division lemma to get

46 = 23 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 299 and 782 is 23

Notice that 23 = HCF(46,23) = HCF(69,46) = HCF(115,69) = HCF(184,115) = HCF(299,184) = HCF(782,299) .

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

Step 1: Since 372 > 23, we apply the division lemma to 372 and 23, to get

372 = 23 x 16 + 4

Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 4 and 23, to get

23 = 4 x 5 + 3

Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get

4 = 3 x 1 + 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 23 and 372 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(372,23) .

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Frequently Asked Questions on HCF of 299, 782, 372 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 299, 782, 372?

Answer: HCF of 299, 782, 372 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 299, 782, 372 using Euclid's Algorithm?

Answer: For arbitrary numbers 299, 782, 372 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.