Highest Common Factor of 648, 374, 285 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 648, 374, 285 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 648, 374, 285 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 648, 374, 285 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 648, 374, 285 is 1.

HCF(648, 374, 285) = 1

HCF of 648, 374, 285 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 648, 374, 285 is 1.

Highest Common Factor of 648,374,285 using Euclid's algorithm

Highest Common Factor of 648,374,285 is 1

Step 1: Since 648 > 374, we apply the division lemma to 648 and 374, to get

648 = 374 x 1 + 274

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 274 and 374, to get

374 = 274 x 1 + 100

Step 3: We consider the new divisor 274 and the new remainder 100, and apply the division lemma to get

274 = 100 x 2 + 74

We consider the new divisor 100 and the new remainder 74,and apply the division lemma to get

100 = 74 x 1 + 26

We consider the new divisor 74 and the new remainder 26,and apply the division lemma to get

74 = 26 x 2 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 648 and 374 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(74,26) = HCF(100,74) = HCF(274,100) = HCF(374,274) = HCF(648,374) .

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

Step 1: Since 285 > 2, we apply the division lemma to 285 and 2, to get

285 = 2 x 142 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 285 is 1

Notice that 1 = HCF(2,1) = HCF(285,2) .

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Frequently Asked Questions on HCF of 648, 374, 285 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 648, 374, 285?

Answer: HCF of 648, 374, 285 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 648, 374, 285 using Euclid's Algorithm?

Answer: For arbitrary numbers 648, 374, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.