Highest Common Factor of 746, 1284, 1918 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 746, 1284, 1918 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 746, 1284, 1918 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 746, 1284, 1918 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 746, 1284, 1918 is 2.

HCF(746, 1284, 1918) = 2

HCF of 746, 1284, 1918 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 746, 1284, 1918 is 2.

Highest Common Factor of 746,1284,1918 using Euclid's algorithm

Highest Common Factor of 746,1284,1918 is 2

Step 1: Since 1284 > 746, we apply the division lemma to 1284 and 746, to get

1284 = 746 x 1 + 538

Step 2: Since the reminder 746 ≠ 0, we apply division lemma to 538 and 746, to get

746 = 538 x 1 + 208

Step 3: We consider the new divisor 538 and the new remainder 208, and apply the division lemma to get

538 = 208 x 2 + 122

We consider the new divisor 208 and the new remainder 122,and apply the division lemma to get

208 = 122 x 1 + 86

We consider the new divisor 122 and the new remainder 86,and apply the division lemma to get

122 = 86 x 1 + 36

We consider the new divisor 86 and the new remainder 36,and apply the division lemma to get

86 = 36 x 2 + 14

We consider the new divisor 36 and the new remainder 14,and apply the division lemma to get

36 = 14 x 2 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 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 746 and 1284 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(36,14) = HCF(86,36) = HCF(122,86) = HCF(208,122) = HCF(538,208) = HCF(746,538) = HCF(1284,746) .

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

Step 1: Since 1918 > 2, we apply the division lemma to 1918 and 2, to get

1918 = 2 x 959 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 1918 is 2

Notice that 2 = HCF(1918,2) .

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Frequently Asked Questions on HCF of 746, 1284, 1918 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 746, 1284, 1918?

Answer: HCF of 746, 1284, 1918 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 746, 1284, 1918 using Euclid's Algorithm?

Answer: For arbitrary numbers 746, 1284, 1918 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.