Highest Common Factor of 670, 795, 563 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 670, 795, 563 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 670, 795, 563 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 670, 795, 563 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 670, 795, 563 is 1.

HCF(670, 795, 563) = 1

HCF of 670, 795, 563 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 670, 795, 563 is 1.

Highest Common Factor of 670,795,563 using Euclid's algorithm

Highest Common Factor of 670,795,563 is 1

Step 1: Since 795 > 670, we apply the division lemma to 795 and 670, to get

795 = 670 x 1 + 125

Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 125 and 670, to get

670 = 125 x 5 + 45

Step 3: We consider the new divisor 125 and the new remainder 45, and apply the division lemma to get

125 = 45 x 2 + 35

We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get

45 = 35 x 1 + 10

We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get

35 = 10 x 3 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 670 and 795 is 5

Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(125,45) = HCF(670,125) = HCF(795,670) .

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

Step 1: Since 563 > 5, we apply the division lemma to 563 and 5, to get

563 = 5 x 112 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

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

3 = 2 x 1 + 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 5 and 563 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(563,5) .

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Frequently Asked Questions on HCF of 670, 795, 563 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 670, 795, 563?

Answer: HCF of 670, 795, 563 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 670, 795, 563 using Euclid's Algorithm?

Answer: For arbitrary numbers 670, 795, 563 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.