Highest Common Factor of 827, 148, 24 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 827, 148, 24 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 827, 148, 24 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 827, 148, 24 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 827, 148, 24 is 1.

HCF(827, 148, 24) = 1

HCF of 827, 148, 24 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 827, 148, 24 is 1.

Highest Common Factor of 827,148,24 using Euclid's algorithm

Highest Common Factor of 827,148,24 is 1

Step 1: Since 827 > 148, we apply the division lemma to 827 and 148, to get

827 = 148 x 5 + 87

Step 2: Since the reminder 148 ≠ 0, we apply division lemma to 87 and 148, to get

148 = 87 x 1 + 61

Step 3: We consider the new divisor 87 and the new remainder 61, and apply the division lemma to get

87 = 61 x 1 + 26

We consider the new divisor 61 and the new remainder 26,and apply the division lemma to get

61 = 26 x 2 + 9

We consider the new divisor 26 and the new remainder 9,and apply the division lemma to get

26 = 9 x 2 + 8

We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get

9 = 8 x 1 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 827 and 148 is 1

Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(26,9) = HCF(61,26) = HCF(87,61) = HCF(148,87) = HCF(827,148) .

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

Step 1: Since 24 > 1, we apply the division lemma to 24 and 1, to get

24 = 1 x 24 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 24 is 1

Notice that 1 = HCF(24,1) .

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Frequently Asked Questions on HCF of 827, 148, 24 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 827, 148, 24?

Answer: HCF of 827, 148, 24 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 827, 148, 24 using Euclid's Algorithm?

Answer: For arbitrary numbers 827, 148, 24 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.