Highest Common Factor of 409, 673, 505, 77 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 409, 673, 505, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 409, 673, 505, 77 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 409, 673, 505, 77 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 409, 673, 505, 77 is 1.

HCF(409, 673, 505, 77) = 1

HCF of 409, 673, 505, 77 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 409, 673, 505, 77 is 1.

Highest Common Factor of 409,673,505,77 using Euclid's algorithm

Highest Common Factor of 409,673,505,77 is 1

Step 1: Since 673 > 409, we apply the division lemma to 673 and 409, to get

673 = 409 x 1 + 264

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 264 and 409, to get

409 = 264 x 1 + 145

Step 3: We consider the new divisor 264 and the new remainder 145, and apply the division lemma to get

264 = 145 x 1 + 119

We consider the new divisor 145 and the new remainder 119,and apply the division lemma to get

145 = 119 x 1 + 26

We consider the new divisor 119 and the new remainder 26,and apply the division lemma to get

119 = 26 x 4 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 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 409 and 673 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(119,26) = HCF(145,119) = HCF(264,145) = HCF(409,264) = HCF(673,409) .

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

Step 1: Since 505 > 1, we apply the division lemma to 505 and 1, to get

505 = 1 x 505 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 505 is 1

Notice that 1 = HCF(505,1) .

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

Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get

77 = 1 x 77 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1

Notice that 1 = HCF(77,1) .

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Frequently Asked Questions on HCF of 409, 673, 505, 77 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 409, 673, 505, 77?

Answer: HCF of 409, 673, 505, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 409, 673, 505, 77 using Euclid's Algorithm?

Answer: For arbitrary numbers 409, 673, 505, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.