Highest Common Factor of 465, 792, 44 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 465, 792, 44 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 465, 792, 44 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 465, 792, 44 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 465, 792, 44 is 1.

HCF(465, 792, 44) = 1

HCF of 465, 792, 44 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 465, 792, 44 is 1.

Highest Common Factor of 465,792,44 using Euclid's algorithm

Highest Common Factor of 465,792,44 is 1

Step 1: Since 792 > 465, we apply the division lemma to 792 and 465, to get

792 = 465 x 1 + 327

Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 327 and 465, to get

465 = 327 x 1 + 138

Step 3: We consider the new divisor 327 and the new remainder 138, and apply the division lemma to get

327 = 138 x 2 + 51

We consider the new divisor 138 and the new remainder 51,and apply the division lemma to get

138 = 51 x 2 + 36

We consider the new divisor 51 and the new remainder 36,and apply the division lemma to get

51 = 36 x 1 + 15

We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get

36 = 15 x 2 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 465 and 792 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(138,51) = HCF(327,138) = HCF(465,327) = HCF(792,465) .

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

Step 1: Since 44 > 3, we apply the division lemma to 44 and 3, to get

44 = 3 x 14 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 44 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(44,3) .

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Frequently Asked Questions on HCF of 465, 792, 44 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 465, 792, 44?

Answer: HCF of 465, 792, 44 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 465, 792, 44 using Euclid's Algorithm?

Answer: For arbitrary numbers 465, 792, 44 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.