Highest Common Factor of 624, 274, 148 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 624, 274, 148 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 624, 274, 148 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 624, 274, 148 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 624, 274, 148 is 2.

HCF(624, 274, 148) = 2

HCF of 624, 274, 148 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 624, 274, 148 is 2.

Highest Common Factor of 624,274,148 using Euclid's algorithm

Highest Common Factor of 624,274,148 is 2

Step 1: Since 624 > 274, we apply the division lemma to 624 and 274, to get

624 = 274 x 2 + 76

Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 76 and 274, to get

274 = 76 x 3 + 46

Step 3: We consider the new divisor 76 and the new remainder 46, and apply the division lemma to get

76 = 46 x 1 + 30

We consider the new divisor 46 and the new remainder 30,and apply the division lemma to get

46 = 30 x 1 + 16

We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get

30 = 16 x 1 + 14

We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get

16 = 14 x 1 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 624 and 274 is 2

Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(46,30) = HCF(76,46) = HCF(274,76) = HCF(624,274) .

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

Step 1: Since 148 > 2, we apply the division lemma to 148 and 2, to get

148 = 2 x 74 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 148 is 2

Notice that 2 = HCF(148,2) .

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Frequently Asked Questions on HCF of 624, 274, 148 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 624, 274, 148?

Answer: HCF of 624, 274, 148 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 624, 274, 148 using Euclid's Algorithm?

Answer: For arbitrary numbers 624, 274, 148 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.