Highest Common Factor of 675, 495, 746 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 675, 495, 746 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 495, 746 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 675, 495, 746 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 675, 495, 746 is 1.

HCF(675, 495, 746) = 1

HCF of 675, 495, 746 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 675, 495, 746 is 1.

Highest Common Factor of 675,495,746 using Euclid's algorithm

Highest Common Factor of 675,495,746 is 1

Step 1: Since 675 > 495, we apply the division lemma to 675 and 495, to get

675 = 495 x 1 + 180

Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 180 and 495, to get

495 = 180 x 2 + 135

Step 3: We consider the new divisor 180 and the new remainder 135, and apply the division lemma to get

180 = 135 x 1 + 45

We consider the new divisor 135 and the new remainder 45, and apply the division lemma to get

135 = 45 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 675 and 495 is 45

Notice that 45 = HCF(135,45) = HCF(180,135) = HCF(495,180) = HCF(675,495) .

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

Step 1: Since 746 > 45, we apply the division lemma to 746 and 45, to get

746 = 45 x 16 + 26

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 26 and 45, to get

45 = 26 x 1 + 19

Step 3: We consider the new divisor 26 and the new remainder 19, and apply the division lemma to get

26 = 19 x 1 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 45 and 746 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(45,26) = HCF(746,45) .

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Frequently Asked Questions on HCF of 675, 495, 746 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 675, 495, 746?

Answer: HCF of 675, 495, 746 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 495, 746 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 495, 746 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.