Highest Common Factor of 420, 223, 110, 356 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 420, 223, 110, 356 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 223, 110, 356 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 420, 223, 110, 356 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 420, 223, 110, 356 is 1.

HCF(420, 223, 110, 356) = 1

HCF of 420, 223, 110, 356 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 420, 223, 110, 356 is 1.

Highest Common Factor of 420,223,110,356 using Euclid's algorithm

Highest Common Factor of 420,223,110,356 is 1

Step 1: Since 420 > 223, we apply the division lemma to 420 and 223, to get

420 = 223 x 1 + 197

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 197 and 223, to get

223 = 197 x 1 + 26

Step 3: We consider the new divisor 197 and the new remainder 26, and apply the division lemma to get

197 = 26 x 7 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 420 and 223 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(197,26) = HCF(223,197) = HCF(420,223) .

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

Step 1: Since 110 > 1, we apply the division lemma to 110 and 1, to get

110 = 1 x 110 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 110 is 1

Notice that 1 = HCF(110,1) .

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

Step 1: Since 356 > 1, we apply the division lemma to 356 and 1, to get

356 = 1 x 356 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 356 is 1

Notice that 1 = HCF(356,1) .

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Frequently Asked Questions on HCF of 420, 223, 110, 356 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 420, 223, 110, 356?

Answer: HCF of 420, 223, 110, 356 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 223, 110, 356 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 223, 110, 356 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.