Highest Common Factor of 423, 612, 553 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 423, 612, 553 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 423, 612, 553 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 423, 612, 553 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 423, 612, 553 is 1.

HCF(423, 612, 553) = 1

HCF of 423, 612, 553 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 423, 612, 553 is 1.

Highest Common Factor of 423,612,553 using Euclid's algorithm

Highest Common Factor of 423,612,553 is 1

Step 1: Since 612 > 423, we apply the division lemma to 612 and 423, to get

612 = 423 x 1 + 189

Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 189 and 423, to get

423 = 189 x 2 + 45

Step 3: We consider the new divisor 189 and the new remainder 45, and apply the division lemma to get

189 = 45 x 4 + 9

We consider the new divisor 45 and the new remainder 9, and apply the division lemma to get

45 = 9 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 423 and 612 is 9

Notice that 9 = HCF(45,9) = HCF(189,45) = HCF(423,189) = HCF(612,423) .

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

Step 1: Since 553 > 9, we apply the division lemma to 553 and 9, to get

553 = 9 x 61 + 4

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 4 and 9, to get

9 = 4 x 2 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 553 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(553,9) .

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Frequently Asked Questions on HCF of 423, 612, 553 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 423, 612, 553?

Answer: HCF of 423, 612, 553 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 423, 612, 553 using Euclid's Algorithm?

Answer: For arbitrary numbers 423, 612, 553 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.