Highest Common Factor of 7021, 9000 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 7021, 9000 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7021, 9000 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 7021, 9000 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 7021, 9000 is 1.

HCF(7021, 9000) = 1

HCF of 7021, 9000 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 7021, 9000 is 1.

Highest Common Factor of 7021,9000 using Euclid's algorithm

Highest Common Factor of 7021,9000 is 1

Step 1: Since 9000 > 7021, we apply the division lemma to 9000 and 7021, to get

9000 = 7021 x 1 + 1979

Step 2: Since the reminder 7021 ≠ 0, we apply division lemma to 1979 and 7021, to get

7021 = 1979 x 3 + 1084

Step 3: We consider the new divisor 1979 and the new remainder 1084, and apply the division lemma to get

1979 = 1084 x 1 + 895

We consider the new divisor 1084 and the new remainder 895,and apply the division lemma to get

1084 = 895 x 1 + 189

We consider the new divisor 895 and the new remainder 189,and apply the division lemma to get

895 = 189 x 4 + 139

We consider the new divisor 189 and the new remainder 139,and apply the division lemma to get

189 = 139 x 1 + 50

We consider the new divisor 139 and the new remainder 50,and apply the division lemma to get

139 = 50 x 2 + 39

We consider the new divisor 50 and the new remainder 39,and apply the division lemma to get

50 = 39 x 1 + 11

We consider the new divisor 39 and the new remainder 11,and apply the division lemma to get

39 = 11 x 3 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7021 and 9000 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(39,11) = HCF(50,39) = HCF(139,50) = HCF(189,139) = HCF(895,189) = HCF(1084,895) = HCF(1979,1084) = HCF(7021,1979) = HCF(9000,7021) .

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Frequently Asked Questions on HCF of 7021, 9000 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 7021, 9000?

Answer: HCF of 7021, 9000 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7021, 9000 using Euclid's Algorithm?

Answer: For arbitrary numbers 7021, 9000 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.