Highest Common Factor of 912, 624, 649 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 912, 624, 649 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 912, 624, 649 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 912, 624, 649 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 912, 624, 649 is 1.

HCF(912, 624, 649) = 1

HCF of 912, 624, 649 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 912, 624, 649 is 1.

Highest Common Factor of 912,624,649 using Euclid's algorithm

Highest Common Factor of 912,624,649 is 1

Step 1: Since 912 > 624, we apply the division lemma to 912 and 624, to get

912 = 624 x 1 + 288

Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 288 and 624, to get

624 = 288 x 2 + 48

Step 3: We consider the new divisor 288 and the new remainder 48, and apply the division lemma to get

288 = 48 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 912 and 624 is 48

Notice that 48 = HCF(288,48) = HCF(624,288) = HCF(912,624) .

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

Step 1: Since 649 > 48, we apply the division lemma to 649 and 48, to get

649 = 48 x 13 + 25

Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 25 and 48, to get

48 = 25 x 1 + 23

Step 3: We consider the new divisor 25 and the new remainder 23, and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 48 and 649 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(649,48) .

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Frequently Asked Questions on HCF of 912, 624, 649 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 912, 624, 649?

Answer: HCF of 912, 624, 649 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 912, 624, 649 using Euclid's Algorithm?

Answer: For arbitrary numbers 912, 624, 649 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.