Highest Common Factor of 554, 689, 177 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 554, 689, 177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 554, 689, 177 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 554, 689, 177 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 554, 689, 177 is 1.

HCF(554, 689, 177) = 1

HCF of 554, 689, 177 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 554, 689, 177 is 1.

Highest Common Factor of 554,689,177 using Euclid's algorithm

Highest Common Factor of 554,689,177 is 1

Step 1: Since 689 > 554, we apply the division lemma to 689 and 554, to get

689 = 554 x 1 + 135

Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 135 and 554, to get

554 = 135 x 4 + 14

Step 3: We consider the new divisor 135 and the new remainder 14, and apply the division lemma to get

135 = 14 x 9 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

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 554 and 689 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(135,14) = HCF(554,135) = HCF(689,554) .

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

Step 1: Since 177 > 1, we apply the division lemma to 177 and 1, to get

177 = 1 x 177 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 177 is 1

Notice that 1 = HCF(177,1) .

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Frequently Asked Questions on HCF of 554, 689, 177 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 554, 689, 177?

Answer: HCF of 554, 689, 177 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 554, 689, 177 using Euclid's Algorithm?

Answer: For arbitrary numbers 554, 689, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.