Highest Common Factor of 880, 653, 21 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, 653, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 880, 653, 21 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, 653, 21 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, 653, 21 is 1.

HCF(880, 653, 21) = 1

HCF of 880, 653, 21 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, 653, 21 is 1.

Highest Common Factor of 880,653,21 using Euclid's algorithm

Highest Common Factor of 880,653,21 is 1

Step 1: Since 880 > 653, we apply the division lemma to 880 and 653, to get

880 = 653 x 1 + 227

Step 2: Since the reminder 653 ≠ 0, we apply division lemma to 227 and 653, to get

653 = 227 x 2 + 199

Step 3: We consider the new divisor 227 and the new remainder 199, and apply the division lemma to get

227 = 199 x 1 + 28

We consider the new divisor 199 and the new remainder 28,and apply the division lemma to get

199 = 28 x 7 + 3

We consider the new divisor 28 and the new remainder 3,and apply the division lemma to get

28 = 3 x 9 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 880 and 653 is 1

Notice that 1 = HCF(3,1) = HCF(28,3) = HCF(199,28) = HCF(227,199) = HCF(653,227) = HCF(880,653) .

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

Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1

Notice that 1 = HCF(21,1) .

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Frequently Asked Questions on HCF of 880, 653, 21 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, 653, 21?

Answer: HCF of 880, 653, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 880, 653, 21 using Euclid's Algorithm?

Answer: For arbitrary numbers 880, 653, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.