Highest Common Factor of 416, 759, 449 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 416, 759, 449 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 416, 759, 449 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 416, 759, 449 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 416, 759, 449 is 1.

HCF(416, 759, 449) = 1

HCF of 416, 759, 449 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 416, 759, 449 is 1.

Highest Common Factor of 416,759,449 using Euclid's algorithm

Highest Common Factor of 416,759,449 is 1

Step 1: Since 759 > 416, we apply the division lemma to 759 and 416, to get

759 = 416 x 1 + 343

Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 343 and 416, to get

416 = 343 x 1 + 73

Step 3: We consider the new divisor 343 and the new remainder 73, and apply the division lemma to get

343 = 73 x 4 + 51

We consider the new divisor 73 and the new remainder 51,and apply the division lemma to get

73 = 51 x 1 + 22

We consider the new divisor 51 and the new remainder 22,and apply the division lemma to get

51 = 22 x 2 + 7

We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get

22 = 7 x 3 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 416 and 759 is 1

Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(51,22) = HCF(73,51) = HCF(343,73) = HCF(416,343) = HCF(759,416) .

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

Step 1: Since 449 > 1, we apply the division lemma to 449 and 1, to get

449 = 1 x 449 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 449 is 1

Notice that 1 = HCF(449,1) .

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Frequently Asked Questions on HCF of 416, 759, 449 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 416, 759, 449?

Answer: HCF of 416, 759, 449 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 416, 759, 449 using Euclid's Algorithm?

Answer: For arbitrary numbers 416, 759, 449 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.