Highest Common Factor of 667, 554, 559 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 667, 554, 559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 667, 554, 559 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 667, 554, 559 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 667, 554, 559 is 1.

HCF(667, 554, 559) = 1

HCF of 667, 554, 559 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 667, 554, 559 is 1.

Highest Common Factor of 667,554,559 using Euclid's algorithm

Highest Common Factor of 667,554,559 is 1

Step 1: Since 667 > 554, we apply the division lemma to 667 and 554, to get

667 = 554 x 1 + 113

Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 113 and 554, to get

554 = 113 x 4 + 102

Step 3: We consider the new divisor 113 and the new remainder 102, and apply the division lemma to get

113 = 102 x 1 + 11

We consider the new divisor 102 and the new remainder 11,and apply the division lemma to get

102 = 11 x 9 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 667 and 554 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(102,11) = HCF(113,102) = HCF(554,113) = HCF(667,554) .

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

Step 1: Since 559 > 1, we apply the division lemma to 559 and 1, to get

559 = 1 x 559 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 559 is 1

Notice that 1 = HCF(559,1) .

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Frequently Asked Questions on HCF of 667, 554, 559 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 667, 554, 559?

Answer: HCF of 667, 554, 559 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 667, 554, 559 using Euclid's Algorithm?

Answer: For arbitrary numbers 667, 554, 559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.