Highest Common Factor of 443, 998 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 443, 998 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 443, 998 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 443, 998 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 443, 998 is 1.

HCF(443, 998) = 1

HCF of 443, 998 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 443, 998 is 1.

Highest Common Factor of 443,998 using Euclid's algorithm

Highest Common Factor of 443,998 is 1

Step 1: Since 998 > 443, we apply the division lemma to 998 and 443, to get

998 = 443 x 2 + 112

Step 2: Since the reminder 443 ≠ 0, we apply division lemma to 112 and 443, to get

443 = 112 x 3 + 107

Step 3: We consider the new divisor 112 and the new remainder 107, and apply the division lemma to get

112 = 107 x 1 + 5

We consider the new divisor 107 and the new remainder 5,and apply the division lemma to get

107 = 5 x 21 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 443 and 998 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(107,5) = HCF(112,107) = HCF(443,112) = HCF(998,443) .

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Frequently Asked Questions on HCF of 443, 998 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 443, 998?

Answer: HCF of 443, 998 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 443, 998 using Euclid's Algorithm?

Answer: For arbitrary numbers 443, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.