Highest Common Factor of 720, 525, 658 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 720, 525, 658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 720, 525, 658 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 720, 525, 658 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 720, 525, 658 is 1.

HCF(720, 525, 658) = 1

HCF of 720, 525, 658 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 720, 525, 658 is 1.

Highest Common Factor of 720,525,658 using Euclid's algorithm

Highest Common Factor of 720,525,658 is 1

Step 1: Since 720 > 525, we apply the division lemma to 720 and 525, to get

720 = 525 x 1 + 195

Step 2: Since the reminder 525 ≠ 0, we apply division lemma to 195 and 525, to get

525 = 195 x 2 + 135

Step 3: We consider the new divisor 195 and the new remainder 135, and apply the division lemma to get

195 = 135 x 1 + 60

We consider the new divisor 135 and the new remainder 60,and apply the division lemma to get

135 = 60 x 2 + 15

We consider the new divisor 60 and the new remainder 15,and apply the division lemma to get

60 = 15 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 720 and 525 is 15

Notice that 15 = HCF(60,15) = HCF(135,60) = HCF(195,135) = HCF(525,195) = HCF(720,525) .

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

Step 1: Since 658 > 15, we apply the division lemma to 658 and 15, to get

658 = 15 x 43 + 13

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 13 and 15, to get

15 = 13 x 1 + 2

Step 3: We consider the new divisor 13 and the new remainder 2, and apply the division lemma to get

13 = 2 x 6 + 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 15 and 658 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(658,15) .

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Frequently Asked Questions on HCF of 720, 525, 658 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 720, 525, 658?

Answer: HCF of 720, 525, 658 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 720, 525, 658 using Euclid's Algorithm?

Answer: For arbitrary numbers 720, 525, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.