Highest Common Factor of 507, 377, 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 507, 377, 660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 507, 377, 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 507, 377, 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 507, 377, 660 is 1.

HCF(507, 377, 660) = 1

HCF of 507, 377, 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 507, 377, 660 is 1.

Highest Common Factor of 507,377,660 using Euclid's algorithm

Highest Common Factor of 507,377,660 is 1

Step 1: Since 507 > 377, we apply the division lemma to 507 and 377, to get

507 = 377 x 1 + 130

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 130 and 377, to get

377 = 130 x 2 + 117

Step 3: We consider the new divisor 130 and the new remainder 117, and apply the division lemma to get

130 = 117 x 1 + 13

We consider the new divisor 117 and the new remainder 13, and apply the division lemma to get

117 = 13 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 507 and 377 is 13

Notice that 13 = HCF(117,13) = HCF(130,117) = HCF(377,130) = HCF(507,377) .

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

Step 1: Since 660 > 13, we apply the division lemma to 660 and 13, to get

660 = 13 x 50 + 10

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 10 and 13, to get

13 = 10 x 1 + 3

Step 3: We consider the new divisor 10 and the new remainder 3, and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 660 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(660,13) .

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Frequently Asked Questions on HCF of 507, 377, 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 507, 377, 660?

Answer: HCF of 507, 377, 660 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 507, 377, 660 using Euclid's Algorithm?

Answer: For arbitrary numbers 507, 377, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.