Highest Common Factor of 148, 3922, 6465 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 148, 3922, 6465 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 148, 3922, 6465 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 148, 3922, 6465 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 148, 3922, 6465 is 1.

HCF(148, 3922, 6465) = 1

HCF of 148, 3922, 6465 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 148, 3922, 6465 is 1.

Highest Common Factor of 148,3922,6465 using Euclid's algorithm

Highest Common Factor of 148,3922,6465 is 1

Step 1: Since 3922 > 148, we apply the division lemma to 3922 and 148, to get

3922 = 148 x 26 + 74

Step 2: Since the reminder 148 ≠ 0, we apply division lemma to 74 and 148, to get

148 = 74 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 74, the HCF of 148 and 3922 is 74

Notice that 74 = HCF(148,74) = HCF(3922,148) .

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

Step 1: Since 6465 > 74, we apply the division lemma to 6465 and 74, to get

6465 = 74 x 87 + 27

Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 27 and 74, to get

74 = 27 x 2 + 20

Step 3: We consider the new divisor 27 and the new remainder 20, and apply the division lemma to get

27 = 20 x 1 + 7

We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get

20 = 7 x 2 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 74 and 6465 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(74,27) = HCF(6465,74) .

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Frequently Asked Questions on HCF of 148, 3922, 6465 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 148, 3922, 6465?

Answer: HCF of 148, 3922, 6465 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 148, 3922, 6465 using Euclid's Algorithm?

Answer: For arbitrary numbers 148, 3922, 6465 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.