Highest Common Factor of 449, 778, 577 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 449, 778, 577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 449, 778, 577 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 449, 778, 577 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 449, 778, 577 is 1.

HCF(449, 778, 577) = 1

HCF of 449, 778, 577 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 449, 778, 577 is 1.

Highest Common Factor of 449,778,577 using Euclid's algorithm

Highest Common Factor of 449,778,577 is 1

Step 1: Since 778 > 449, we apply the division lemma to 778 and 449, to get

778 = 449 x 1 + 329

Step 2: Since the reminder 449 ≠ 0, we apply division lemma to 329 and 449, to get

449 = 329 x 1 + 120

Step 3: We consider the new divisor 329 and the new remainder 120, and apply the division lemma to get

329 = 120 x 2 + 89

We consider the new divisor 120 and the new remainder 89,and apply the division lemma to get

120 = 89 x 1 + 31

We consider the new divisor 89 and the new remainder 31,and apply the division lemma to get

89 = 31 x 2 + 27

We consider the new divisor 31 and the new remainder 27,and apply the division lemma to get

31 = 27 x 1 + 4

We consider the new divisor 27 and the new remainder 4,and apply the division lemma to get

27 = 4 x 6 + 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 449 and 778 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) = HCF(31,27) = HCF(89,31) = HCF(120,89) = HCF(329,120) = HCF(449,329) = HCF(778,449) .

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

Step 1: Since 577 > 1, we apply the division lemma to 577 and 1, to get

577 = 1 x 577 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 577 is 1

Notice that 1 = HCF(577,1) .

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Frequently Asked Questions on HCF of 449, 778, 577 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 449, 778, 577?

Answer: HCF of 449, 778, 577 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 449, 778, 577 using Euclid's Algorithm?

Answer: For arbitrary numbers 449, 778, 577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.