Highest Common Factor of 553, 342, 438 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 553, 342, 438 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 553, 342, 438 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 553, 342, 438 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 553, 342, 438 is 1.

HCF(553, 342, 438) = 1

HCF of 553, 342, 438 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 553, 342, 438 is 1.

Highest Common Factor of 553,342,438 using Euclid's algorithm

Highest Common Factor of 553,342,438 is 1

Step 1: Since 553 > 342, we apply the division lemma to 553 and 342, to get

553 = 342 x 1 + 211

Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 211 and 342, to get

342 = 211 x 1 + 131

Step 3: We consider the new divisor 211 and the new remainder 131, and apply the division lemma to get

211 = 131 x 1 + 80

We consider the new divisor 131 and the new remainder 80,and apply the division lemma to get

131 = 80 x 1 + 51

We consider the new divisor 80 and the new remainder 51,and apply the division lemma to get

80 = 51 x 1 + 29

We consider the new divisor 51 and the new remainder 29,and apply the division lemma to get

51 = 29 x 1 + 22

We consider the new divisor 29 and the new remainder 22,and apply the division lemma to get

29 = 22 x 1 + 7

We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get

22 = 7 x 3 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 553 and 342 is 1

Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(29,22) = HCF(51,29) = HCF(80,51) = HCF(131,80) = HCF(211,131) = HCF(342,211) = HCF(553,342) .

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

Step 1: Since 438 > 1, we apply the division lemma to 438 and 1, to get

438 = 1 x 438 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 438 is 1

Notice that 1 = HCF(438,1) .

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Frequently Asked Questions on HCF of 553, 342, 438 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 553, 342, 438?

Answer: HCF of 553, 342, 438 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 553, 342, 438 using Euclid's Algorithm?

Answer: For arbitrary numbers 553, 342, 438 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.