Highest Common Factor of 644, 737, 678 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 644, 737, 678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 644, 737, 678 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 644, 737, 678 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 644, 737, 678 is 1.

HCF(644, 737, 678) = 1

HCF of 644, 737, 678 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 644, 737, 678 is 1.

Highest Common Factor of 644,737,678 using Euclid's algorithm

Highest Common Factor of 644,737,678 is 1

Step 1: Since 737 > 644, we apply the division lemma to 737 and 644, to get

737 = 644 x 1 + 93

Step 2: Since the reminder 644 ≠ 0, we apply division lemma to 93 and 644, to get

644 = 93 x 6 + 86

Step 3: We consider the new divisor 93 and the new remainder 86, and apply the division lemma to get

93 = 86 x 1 + 7

We consider the new divisor 86 and the new remainder 7,and apply the division lemma to get

86 = 7 x 12 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 644 and 737 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(86,7) = HCF(93,86) = HCF(644,93) = HCF(737,644) .

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

Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get

678 = 1 x 678 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1

Notice that 1 = HCF(678,1) .

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Frequently Asked Questions on HCF of 644, 737, 678 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 644, 737, 678?

Answer: HCF of 644, 737, 678 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 644, 737, 678 using Euclid's Algorithm?

Answer: For arbitrary numbers 644, 737, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.