Highest Common Factor of 560, 154, 205 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, 154, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 560, 154, 205 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, 154, 205 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, 154, 205 is 1.

HCF(560, 154, 205) = 1

HCF of 560, 154, 205 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, 154, 205 is 1.

Highest Common Factor of 560,154,205 using Euclid's algorithm

Highest Common Factor of 560,154,205 is 1

Step 1: Since 560 > 154, we apply the division lemma to 560 and 154, to get

560 = 154 x 3 + 98

Step 2: Since the reminder 154 ≠ 0, we apply division lemma to 98 and 154, to get

154 = 98 x 1 + 56

Step 3: We consider the new divisor 98 and the new remainder 56, and apply the division lemma to get

98 = 56 x 1 + 42

We consider the new divisor 56 and the new remainder 42,and apply the division lemma to get

56 = 42 x 1 + 14

We consider the new divisor 42 and the new remainder 14,and apply the division lemma to get

42 = 14 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 560 and 154 is 14

Notice that 14 = HCF(42,14) = HCF(56,42) = HCF(98,56) = HCF(154,98) = HCF(560,154) .

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

Step 1: Since 205 > 14, we apply the division lemma to 205 and 14, to get

205 = 14 x 14 + 9

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 9 and 14, to get

14 = 9 x 1 + 5

Step 3: We consider the new divisor 9 and the new remainder 5, and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 205 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(205,14) .

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Frequently Asked Questions on HCF of 560, 154, 205 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, 154, 205?

Answer: HCF of 560, 154, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 560, 154, 205 using Euclid's Algorithm?

Answer: For arbitrary numbers 560, 154, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.