Highest Common Factor of 560, 664, 869, 546 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 560, 664, 869, 546 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 664, 869, 546 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 560, 664, 869, 546 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 560, 664, 869, 546 is 1.

HCF(560, 664, 869, 546) = 1

HCF of 560, 664, 869, 546 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 560, 664, 869, 546 is 1.

Highest Common Factor of 560,664,869,546 using Euclid's algorithm

Highest Common Factor of 560,664,869,546 is 1

Step 1: Since 664 > 560, we apply the division lemma to 664 and 560, to get

664 = 560 x 1 + 104

Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 104 and 560, to get

560 = 104 x 5 + 40

Step 3: We consider the new divisor 104 and the new remainder 40, and apply the division lemma to get

104 = 40 x 2 + 24

We consider the new divisor 40 and the new remainder 24,and apply the division lemma to get

40 = 24 x 1 + 16

We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get

24 = 16 x 1 + 8

We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 560 and 664 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(40,24) = HCF(104,40) = HCF(560,104) = HCF(664,560) .

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

Step 1: Since 869 > 8, we apply the division lemma to 869 and 8, to get

869 = 8 x 108 + 5

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get

8 = 5 x 1 + 3

Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 869 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(869,8) .

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

Step 1: Since 546 > 1, we apply the division lemma to 546 and 1, to get

546 = 1 x 546 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 546 is 1

Notice that 1 = HCF(546,1) .

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Frequently Asked Questions on HCF of 560, 664, 869, 546 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 560, 664, 869, 546?

Answer: HCF of 560, 664, 869, 546 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 664, 869, 546 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 664, 869, 546 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.