Highest Common Factor of 821, 602, 127 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 821, 602, 127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 821, 602, 127 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 821, 602, 127 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 821, 602, 127 is 1.

HCF(821, 602, 127) = 1

HCF of 821, 602, 127 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 821, 602, 127 is 1.

Highest Common Factor of 821,602,127 using Euclid's algorithm

Highest Common Factor of 821,602,127 is 1

Step 1: Since 821 > 602, we apply the division lemma to 821 and 602, to get

821 = 602 x 1 + 219

Step 2: Since the reminder 602 ≠ 0, we apply division lemma to 219 and 602, to get

602 = 219 x 2 + 164

Step 3: We consider the new divisor 219 and the new remainder 164, and apply the division lemma to get

219 = 164 x 1 + 55

We consider the new divisor 164 and the new remainder 55,and apply the division lemma to get

164 = 55 x 2 + 54

We consider the new divisor 55 and the new remainder 54,and apply the division lemma to get

55 = 54 x 1 + 1

We consider the new divisor 54 and the new remainder 1,and apply the division lemma to get

54 = 1 x 54 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 602 is 1

Notice that 1 = HCF(54,1) = HCF(55,54) = HCF(164,55) = HCF(219,164) = HCF(602,219) = HCF(821,602) .

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

Step 1: Since 127 > 1, we apply the division lemma to 127 and 1, to get

127 = 1 x 127 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 127 is 1

Notice that 1 = HCF(127,1) .

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Frequently Asked Questions on HCF of 821, 602, 127 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 821, 602, 127?

Answer: HCF of 821, 602, 127 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 821, 602, 127 using Euclid's Algorithm?

Answer: For arbitrary numbers 821, 602, 127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.