Highest Common Factor of 824, 652, 914, 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 824, 652, 914, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 824, 652, 914, 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 824, 652, 914, 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 824, 652, 914, 21 is 1.

HCF(824, 652, 914, 21) = 1

HCF of 824, 652, 914, 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 824, 652, 914, 21 is 1.

Highest Common Factor of 824,652,914,21 using Euclid's algorithm

Highest Common Factor of 824,652,914,21 is 1

Step 1: Since 824 > 652, we apply the division lemma to 824 and 652, to get

824 = 652 x 1 + 172

Step 2: Since the reminder 652 ≠ 0, we apply division lemma to 172 and 652, to get

652 = 172 x 3 + 136

Step 3: We consider the new divisor 172 and the new remainder 136, and apply the division lemma to get

172 = 136 x 1 + 36

We consider the new divisor 136 and the new remainder 36,and apply the division lemma to get

136 = 36 x 3 + 28

We consider the new divisor 36 and the new remainder 28,and apply the division lemma to get

36 = 28 x 1 + 8

We consider the new divisor 28 and the new remainder 8,and apply the division lemma to get

28 = 8 x 3 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 824 and 652 is 4

Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(36,28) = HCF(136,36) = HCF(172,136) = HCF(652,172) = HCF(824,652) .

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

Step 1: Since 914 > 4, we apply the division lemma to 914 and 4, to get

914 = 4 x 228 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 914 is 2

Notice that 2 = HCF(4,2) = HCF(914,4) .

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

Step 1: Since 21 > 2, we apply the division lemma to 21 and 2, to get

21 = 2 x 10 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 21 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) .

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Frequently Asked Questions on HCF of 824, 652, 914, 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 824, 652, 914, 21?

Answer: HCF of 824, 652, 914, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 824, 652, 914, 21 using Euclid's Algorithm?

Answer: For arbitrary numbers 824, 652, 914, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.