Highest Common Factor of 752, 495, 660 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 752, 495, 660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 752, 495, 660 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 752, 495, 660 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 752, 495, 660 is 1.

HCF(752, 495, 660) = 1

HCF of 752, 495, 660 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 752, 495, 660 is 1.

Highest Common Factor of 752,495,660 using Euclid's algorithm

Highest Common Factor of 752,495,660 is 1

Step 1: Since 752 > 495, we apply the division lemma to 752 and 495, to get

752 = 495 x 1 + 257

Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 257 and 495, to get

495 = 257 x 1 + 238

Step 3: We consider the new divisor 257 and the new remainder 238, and apply the division lemma to get

257 = 238 x 1 + 19

We consider the new divisor 238 and the new remainder 19,and apply the division lemma to get

238 = 19 x 12 + 10

We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get

19 = 10 x 1 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 752 and 495 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(238,19) = HCF(257,238) = HCF(495,257) = HCF(752,495) .

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

Step 1: Since 660 > 1, we apply the division lemma to 660 and 1, to get

660 = 1 x 660 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 660 is 1

Notice that 1 = HCF(660,1) .

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Frequently Asked Questions on HCF of 752, 495, 660 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 752, 495, 660?

Answer: HCF of 752, 495, 660 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 752, 495, 660 using Euclid's Algorithm?

Answer: For arbitrary numbers 752, 495, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.