Highest Common Factor of 513, 713, 664, 722 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, 713, 664, 722 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 513, 713, 664, 722 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, 713, 664, 722 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, 713, 664, 722 is 1.

HCF(513, 713, 664, 722) = 1

HCF of 513, 713, 664, 722 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, 713, 664, 722 is 1.

Highest Common Factor of 513,713,664,722 using Euclid's algorithm

Highest Common Factor of 513,713,664,722 is 1

Step 1: Since 713 > 513, we apply the division lemma to 713 and 513, to get

713 = 513 x 1 + 200

Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 200 and 513, to get

513 = 200 x 2 + 113

Step 3: We consider the new divisor 200 and the new remainder 113, and apply the division lemma to get

200 = 113 x 1 + 87

We consider the new divisor 113 and the new remainder 87,and apply the division lemma to get

113 = 87 x 1 + 26

We consider the new divisor 87 and the new remainder 26,and apply the division lemma to get

87 = 26 x 3 + 9

We consider the new divisor 26 and the new remainder 9,and apply the division lemma to get

26 = 9 x 2 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 513 and 713 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(26,9) = HCF(87,26) = HCF(113,87) = HCF(200,113) = HCF(513,200) = HCF(713,513) .

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

Step 1: Since 664 > 1, we apply the division lemma to 664 and 1, to get

664 = 1 x 664 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 664 is 1

Notice that 1 = HCF(664,1) .

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

Step 1: Since 722 > 1, we apply the division lemma to 722 and 1, to get

722 = 1 x 722 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 722 is 1

Notice that 1 = HCF(722,1) .

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Frequently Asked Questions on HCF of 513, 713, 664, 722 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, 713, 664, 722?

Answer: HCF of 513, 713, 664, 722 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 513, 713, 664, 722 using Euclid's Algorithm?

Answer: For arbitrary numbers 513, 713, 664, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.