Highest Common Factor of 774, 319, 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 774, 319, 174 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 774, 319, 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 774, 319, 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 774, 319, 174 is 1.

HCF(774, 319, 174) = 1

HCF of 774, 319, 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 774, 319, 174 is 1.

Highest Common Factor of 774,319,174 using Euclid's algorithm

Highest Common Factor of 774,319,174 is 1

Step 1: Since 774 > 319, we apply the division lemma to 774 and 319, to get

774 = 319 x 2 + 136

Step 2: Since the reminder 319 ≠ 0, we apply division lemma to 136 and 319, to get

319 = 136 x 2 + 47

Step 3: We consider the new divisor 136 and the new remainder 47, and apply the division lemma to get

136 = 47 x 2 + 42

We consider the new divisor 47 and the new remainder 42,and apply the division lemma to get

47 = 42 x 1 + 5

We consider the new divisor 42 and the new remainder 5,and apply the division lemma to get

42 = 5 x 8 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 774 and 319 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(42,5) = HCF(47,42) = HCF(136,47) = HCF(319,136) = HCF(774,319) .

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 774, 319, 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 774, 319, 174?

Answer: HCF of 774, 319, 174 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 774, 319, 174 using Euclid's Algorithm?

Answer: For arbitrary numbers 774, 319, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.