Highest Common Factor of 513, 746, 977 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 513, 746, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 746, 977 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 513, 746, 977 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 513, 746, 977 is 1.

HCF(513, 746, 977) = 1

HCF of 513, 746, 977 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 513, 746, 977 is 1.

Highest Common Factor of 513,746,977 using Euclid's algorithm

Highest Common Factor of 513,746,977 is 1

Step 1: Since 746 > 513, we apply the division lemma to 746 and 513, to get

746 = 513 x 1 + 233

Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 233 and 513, to get

513 = 233 x 2 + 47

Step 3: We consider the new divisor 233 and the new remainder 47, and apply the division lemma to get

233 = 47 x 4 + 45

We consider the new divisor 47 and the new remainder 45,and apply the division lemma to get

47 = 45 x 1 + 2

We consider the new divisor 45 and the new remainder 2,and apply the division lemma to get

45 = 2 x 22 + 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 513 and 746 is 1

Notice that 1 = HCF(2,1) = HCF(45,2) = HCF(47,45) = HCF(233,47) = HCF(513,233) = HCF(746,513) .

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

Step 1: Since 977 > 1, we apply the division lemma to 977 and 1, to get

977 = 1 x 977 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 977 is 1

Notice that 1 = HCF(977,1) .

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Frequently Asked Questions on HCF of 513, 746, 977 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 513, 746, 977?

Answer: HCF of 513, 746, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 746, 977 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 746, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.