Highest Common Factor of 169, 338, 614 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 169, 338, 614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 169, 338, 614 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 169, 338, 614 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 169, 338, 614 is 1.

HCF(169, 338, 614) = 1

HCF of 169, 338, 614 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 169, 338, 614 is 1.

Highest Common Factor of 169,338,614 using Euclid's algorithm

Highest Common Factor of 169,338,614 is 1

Step 1: Since 338 > 169, we apply the division lemma to 338 and 169, to get

338 = 169 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 169, the HCF of 169 and 338 is 169

Notice that 169 = HCF(338,169) .

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

Step 1: Since 614 > 169, we apply the division lemma to 614 and 169, to get

614 = 169 x 3 + 107

Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 107 and 169, to get

169 = 107 x 1 + 62

Step 3: We consider the new divisor 107 and the new remainder 62, and apply the division lemma to get

107 = 62 x 1 + 45

We consider the new divisor 62 and the new remainder 45,and apply the division lemma to get

62 = 45 x 1 + 17

We consider the new divisor 45 and the new remainder 17,and apply the division lemma to get

45 = 17 x 2 + 11

We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get

17 = 11 x 1 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 169 and 614 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) = HCF(62,45) = HCF(107,62) = HCF(169,107) = HCF(614,169) .

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Frequently Asked Questions on HCF of 169, 338, 614 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 169, 338, 614?

Answer: HCF of 169, 338, 614 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 169, 338, 614 using Euclid's Algorithm?

Answer: For arbitrary numbers 169, 338, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.