Highest Common Factor of 350, 553, 823 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 350, 553, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 350, 553, 823 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 350, 553, 823 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 350, 553, 823 is 1.

HCF(350, 553, 823) = 1

HCF of 350, 553, 823 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 350, 553, 823 is 1.

Highest Common Factor of 350,553,823 using Euclid's algorithm

Highest Common Factor of 350,553,823 is 1

Step 1: Since 553 > 350, we apply the division lemma to 553 and 350, to get

553 = 350 x 1 + 203

Step 2: Since the reminder 350 ≠ 0, we apply division lemma to 203 and 350, to get

350 = 203 x 1 + 147

Step 3: We consider the new divisor 203 and the new remainder 147, and apply the division lemma to get

203 = 147 x 1 + 56

We consider the new divisor 147 and the new remainder 56,and apply the division lemma to get

147 = 56 x 2 + 35

We consider the new divisor 56 and the new remainder 35,and apply the division lemma to get

56 = 35 x 1 + 21

We consider the new divisor 35 and the new remainder 21,and apply the division lemma to get

35 = 21 x 1 + 14

We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get

21 = 14 x 1 + 7

We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get

14 = 7 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 350 and 553 is 7

Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(56,35) = HCF(147,56) = HCF(203,147) = HCF(350,203) = HCF(553,350) .

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

Step 1: Since 823 > 7, we apply the division lemma to 823 and 7, to get

823 = 7 x 117 + 4

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get

7 = 4 x 1 + 3

Step 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 7 and 823 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(823,7) .

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Frequently Asked Questions on HCF of 350, 553, 823 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 350, 553, 823?

Answer: HCF of 350, 553, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 350, 553, 823 using Euclid's Algorithm?

Answer: For arbitrary numbers 350, 553, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.