Highest Common Factor of 249, 459, 748 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 249, 459, 748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 249, 459, 748 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 249, 459, 748 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 249, 459, 748 is 1.

HCF(249, 459, 748) = 1

HCF of 249, 459, 748 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 249, 459, 748 is 1.

Highest Common Factor of 249,459,748 using Euclid's algorithm

Highest Common Factor of 249,459,748 is 1

Step 1: Since 459 > 249, we apply the division lemma to 459 and 249, to get

459 = 249 x 1 + 210

Step 2: Since the reminder 249 ≠ 0, we apply division lemma to 210 and 249, to get

249 = 210 x 1 + 39

Step 3: We consider the new divisor 210 and the new remainder 39, and apply the division lemma to get

210 = 39 x 5 + 15

We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get

39 = 15 x 2 + 9

We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 249 and 459 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(210,39) = HCF(249,210) = HCF(459,249) .

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

Step 1: Since 748 > 3, we apply the division lemma to 748 and 3, to get

748 = 3 x 249 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 748 is 1

Notice that 1 = HCF(3,1) = HCF(748,3) .

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Frequently Asked Questions on HCF of 249, 459, 748 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 249, 459, 748?

Answer: HCF of 249, 459, 748 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 249, 459, 748 using Euclid's Algorithm?

Answer: For arbitrary numbers 249, 459, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.