Highest Common Factor of 44, 66, 699 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 44, 66, 699 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 44, 66, 699 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 44, 66, 699 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 44, 66, 699 is 1.

HCF(44, 66, 699) = 1

HCF of 44, 66, 699 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 44, 66, 699 is 1.

Highest Common Factor of 44,66,699 using Euclid's algorithm

Highest Common Factor of 44,66,699 is 1

Step 1: Since 66 > 44, we apply the division lemma to 66 and 44, to get

66 = 44 x 1 + 22

Step 2: Since the reminder 44 ≠ 0, we apply division lemma to 22 and 44, to get

44 = 22 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 44 and 66 is 22

Notice that 22 = HCF(44,22) = HCF(66,44) .

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

Step 1: Since 699 > 22, we apply the division lemma to 699 and 22, to get

699 = 22 x 31 + 17

Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 17 and 22, to get

22 = 17 x 1 + 5

Step 3: We consider the new divisor 17 and the new remainder 5, and apply the division lemma to get

17 = 5 x 3 + 2

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 22 and 699 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(699,22) .

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Frequently Asked Questions on HCF of 44, 66, 699 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 44, 66, 699?

Answer: HCF of 44, 66, 699 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 44, 66, 699 using Euclid's Algorithm?

Answer: For arbitrary numbers 44, 66, 699 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.