Highest Common Factor of 223, 621, 922, 66 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 223, 621, 922, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 223, 621, 922, 66 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 223, 621, 922, 66 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 223, 621, 922, 66 is 1.

HCF(223, 621, 922, 66) = 1

HCF of 223, 621, 922, 66 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 223, 621, 922, 66 is 1.

Highest Common Factor of 223,621,922,66 using Euclid's algorithm

Highest Common Factor of 223,621,922,66 is 1

Step 1: Since 621 > 223, we apply the division lemma to 621 and 223, to get

621 = 223 x 2 + 175

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 175 and 223, to get

223 = 175 x 1 + 48

Step 3: We consider the new divisor 175 and the new remainder 48, and apply the division lemma to get

175 = 48 x 3 + 31

We consider the new divisor 48 and the new remainder 31,and apply the division lemma to get

48 = 31 x 1 + 17

We consider the new divisor 31 and the new remainder 17,and apply the division lemma to get

31 = 17 x 1 + 14

We consider the new divisor 17 and the new remainder 14,and apply the division lemma to get

17 = 14 x 1 + 3

We consider the new divisor 14 and the new remainder 3,and apply the division lemma to get

14 = 3 x 4 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 223 and 621 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) = HCF(31,17) = HCF(48,31) = HCF(175,48) = HCF(223,175) = HCF(621,223) .

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

Step 1: Since 922 > 1, we apply the division lemma to 922 and 1, to get

922 = 1 x 922 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 922 is 1

Notice that 1 = HCF(922,1) .

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

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

66 = 1 x 66 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1

Notice that 1 = HCF(66,1) .

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Frequently Asked Questions on HCF of 223, 621, 922, 66 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 223, 621, 922, 66?

Answer: HCF of 223, 621, 922, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 223, 621, 922, 66 using Euclid's Algorithm?

Answer: For arbitrary numbers 223, 621, 922, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.