Highest Common Factor of 223, 622, 354 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, 622, 354 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 223, 622, 354 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, 622, 354 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, 622, 354 is 1.

HCF(223, 622, 354) = 1

HCF of 223, 622, 354 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, 622, 354 is 1.

Highest Common Factor of 223,622,354 using Euclid's algorithm

Highest Common Factor of 223,622,354 is 1

Step 1: Since 622 > 223, we apply the division lemma to 622 and 223, to get

622 = 223 x 2 + 176

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 176 and 223, to get

223 = 176 x 1 + 47

Step 3: We consider the new divisor 176 and the new remainder 47, and apply the division lemma to get

176 = 47 x 3 + 35

We consider the new divisor 47 and the new remainder 35,and apply the division lemma to get

47 = 35 x 1 + 12

We consider the new divisor 35 and the new remainder 12,and apply the division lemma to get

35 = 12 x 2 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 223 and 622 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(35,12) = HCF(47,35) = HCF(176,47) = HCF(223,176) = HCF(622,223) .

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

Step 1: Since 354 > 1, we apply the division lemma to 354 and 1, to get

354 = 1 x 354 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 354 is 1

Notice that 1 = HCF(354,1) .

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Frequently Asked Questions on HCF of 223, 622, 354 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, 622, 354?

Answer: HCF of 223, 622, 354 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 223, 622, 354 using Euclid's Algorithm?

Answer: For arbitrary numbers 223, 622, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.