Highest Common Factor of 880, 670, 619 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 880, 670, 619 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 880, 670, 619 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 880, 670, 619 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 880, 670, 619 is 1.

HCF(880, 670, 619) = 1

HCF of 880, 670, 619 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 880, 670, 619 is 1.

Highest Common Factor of 880,670,619 using Euclid's algorithm

Highest Common Factor of 880,670,619 is 1

Step 1: Since 880 > 670, we apply the division lemma to 880 and 670, to get

880 = 670 x 1 + 210

Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 210 and 670, to get

670 = 210 x 3 + 40

Step 3: We consider the new divisor 210 and the new remainder 40, and apply the division lemma to get

210 = 40 x 5 + 10

We consider the new divisor 40 and the new remainder 10, and apply the division lemma to get

40 = 10 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 880 and 670 is 10

Notice that 10 = HCF(40,10) = HCF(210,40) = HCF(670,210) = HCF(880,670) .

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

Step 1: Since 619 > 10, we apply the division lemma to 619 and 10, to get

619 = 10 x 61 + 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 619 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(619,10) .

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Frequently Asked Questions on HCF of 880, 670, 619 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 880, 670, 619?

Answer: HCF of 880, 670, 619 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 880, 670, 619 using Euclid's Algorithm?

Answer: For arbitrary numbers 880, 670, 619 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.