Highest Common Factor of 178, 664, 390 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 178, 664, 390 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 178, 664, 390 is 2 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 178, 664, 390 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 178, 664, 390 is 2.

HCF(178, 664, 390) = 2

HCF of 178, 664, 390 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 178, 664, 390 is 2.

Highest Common Factor of 178,664,390 using Euclid's algorithm

Highest Common Factor of 178,664,390 is 2

Step 1: Since 664 > 178, we apply the division lemma to 664 and 178, to get

664 = 178 x 3 + 130

Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 130 and 178, to get

178 = 130 x 1 + 48

Step 3: We consider the new divisor 130 and the new remainder 48, and apply the division lemma to get

130 = 48 x 2 + 34

We consider the new divisor 48 and the new remainder 34,and apply the division lemma to get

48 = 34 x 1 + 14

We consider the new divisor 34 and the new remainder 14,and apply the division lemma to get

34 = 14 x 2 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 178 and 664 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(34,14) = HCF(48,34) = HCF(130,48) = HCF(178,130) = HCF(664,178) .

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

Step 1: Since 390 > 2, we apply the division lemma to 390 and 2, to get

390 = 2 x 195 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 390 is 2

Notice that 2 = HCF(390,2) .

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Frequently Asked Questions on HCF of 178, 664, 390 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 178, 664, 390?

Answer: HCF of 178, 664, 390 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 178, 664, 390 using Euclid's Algorithm?

Answer: For arbitrary numbers 178, 664, 390 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.