Highest Common Factor of 392, 649, 174 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 392, 649, 174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 392, 649, 174 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 392, 649, 174 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 392, 649, 174 is 1.

HCF(392, 649, 174) = 1

HCF of 392, 649, 174 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 392, 649, 174 is 1.

Highest Common Factor of 392,649,174 using Euclid's algorithm

Highest Common Factor of 392,649,174 is 1

Step 1: Since 649 > 392, we apply the division lemma to 649 and 392, to get

649 = 392 x 1 + 257

Step 2: Since the reminder 392 ≠ 0, we apply division lemma to 257 and 392, to get

392 = 257 x 1 + 135

Step 3: We consider the new divisor 257 and the new remainder 135, and apply the division lemma to get

257 = 135 x 1 + 122

We consider the new divisor 135 and the new remainder 122,and apply the division lemma to get

135 = 122 x 1 + 13

We consider the new divisor 122 and the new remainder 13,and apply the division lemma to get

122 = 13 x 9 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 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 392 and 649 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(122,13) = HCF(135,122) = HCF(257,135) = HCF(392,257) = HCF(649,392) .

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

Step 1: Since 174 > 1, we apply the division lemma to 174 and 1, to get

174 = 1 x 174 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 174 is 1

Notice that 1 = HCF(174,1) .

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Frequently Asked Questions on HCF of 392, 649, 174 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 392, 649, 174?

Answer: HCF of 392, 649, 174 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 392, 649, 174 using Euclid's Algorithm?

Answer: For arbitrary numbers 392, 649, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.