Highest Common Factor of 414, 722, 223, 347 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 414, 722, 223, 347 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 414, 722, 223, 347 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 414, 722, 223, 347 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 414, 722, 223, 347 is 1.

HCF(414, 722, 223, 347) = 1

HCF of 414, 722, 223, 347 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 414, 722, 223, 347 is 1.

Highest Common Factor of 414,722,223,347 using Euclid's algorithm

Highest Common Factor of 414,722,223,347 is 1

Step 1: Since 722 > 414, we apply the division lemma to 722 and 414, to get

722 = 414 x 1 + 308

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 308 and 414, to get

414 = 308 x 1 + 106

Step 3: We consider the new divisor 308 and the new remainder 106, and apply the division lemma to get

308 = 106 x 2 + 96

We consider the new divisor 106 and the new remainder 96,and apply the division lemma to get

106 = 96 x 1 + 10

We consider the new divisor 96 and the new remainder 10,and apply the division lemma to get

96 = 10 x 9 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 414 and 722 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(96,10) = HCF(106,96) = HCF(308,106) = HCF(414,308) = HCF(722,414) .

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

Step 1: Since 223 > 2, we apply the division lemma to 223 and 2, to get

223 = 2 x 111 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 223 is 1

Notice that 1 = HCF(2,1) = HCF(223,2) .

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

Step 1: Since 347 > 1, we apply the division lemma to 347 and 1, to get

347 = 1 x 347 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 347 is 1

Notice that 1 = HCF(347,1) .

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Frequently Asked Questions on HCF of 414, 722, 223, 347 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 414, 722, 223, 347?

Answer: HCF of 414, 722, 223, 347 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 414, 722, 223, 347 using Euclid's Algorithm?

Answer: For arbitrary numbers 414, 722, 223, 347 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.