Highest Common Factor of 984, 828, 221 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 984, 828, 221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 984, 828, 221 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 984, 828, 221 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 984, 828, 221 is 1.

HCF(984, 828, 221) = 1

HCF of 984, 828, 221 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 984, 828, 221 is 1.

Highest Common Factor of 984,828,221 using Euclid's algorithm

Highest Common Factor of 984,828,221 is 1

Step 1: Since 984 > 828, we apply the division lemma to 984 and 828, to get

984 = 828 x 1 + 156

Step 2: Since the reminder 828 ≠ 0, we apply division lemma to 156 and 828, to get

828 = 156 x 5 + 48

Step 3: We consider the new divisor 156 and the new remainder 48, and apply the division lemma to get

156 = 48 x 3 + 12

We consider the new divisor 48 and the new remainder 12, and apply the division lemma to get

48 = 12 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 984 and 828 is 12

Notice that 12 = HCF(48,12) = HCF(156,48) = HCF(828,156) = HCF(984,828) .

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

Step 1: Since 221 > 12, we apply the division lemma to 221 and 12, to get

221 = 12 x 18 + 5

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 5 and 12, to get

12 = 5 x 2 + 2

Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get

5 = 2 x 2 + 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 12 and 221 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(221,12) .

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Frequently Asked Questions on HCF of 984, 828, 221 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 984, 828, 221?

Answer: HCF of 984, 828, 221 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 984, 828, 221 using Euclid's Algorithm?

Answer: For arbitrary numbers 984, 828, 221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.