Highest Common Factor of 670, 720, 219 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, 720, 219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 670, 720, 219 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, 720, 219 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, 720, 219 is 1.

HCF(670, 720, 219) = 1

HCF of 670, 720, 219 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, 720, 219 is 1.

Highest Common Factor of 670,720,219 using Euclid's algorithm

Highest Common Factor of 670,720,219 is 1

Step 1: Since 720 > 670, we apply the division lemma to 720 and 670, to get

720 = 670 x 1 + 50

Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 50 and 670, to get

670 = 50 x 13 + 20

Step 3: We consider the new divisor 50 and the new remainder 20, and apply the division lemma to get

50 = 20 x 2 + 10

We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 670 and 720 is 10

Notice that 10 = HCF(20,10) = HCF(50,20) = HCF(670,50) = HCF(720,670) .

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

Step 1: Since 219 > 10, we apply the division lemma to 219 and 10, to get

219 = 10 x 21 + 9

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 9 and 10, to get

10 = 9 x 1 + 1

Step 3: We consider the new divisor 9 and the new remainder 1, and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 219 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(219,10) .

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Frequently Asked Questions on HCF of 670, 720, 219 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, 720, 219?

Answer: HCF of 670, 720, 219 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 670, 720, 219 using Euclid's Algorithm?

Answer: For arbitrary numbers 670, 720, 219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.