Highest Common Factor of 990, 133 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 990, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 990, 133 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 990, 133 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 990, 133 is 1.

HCF(990, 133) = 1

HCF of 990, 133 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 990, 133 is 1.

Highest Common Factor of 990,133 using Euclid's algorithm

Highest Common Factor of 990,133 is 1

Step 1: Since 990 > 133, we apply the division lemma to 990 and 133, to get

990 = 133 x 7 + 59

Step 2: Since the reminder 133 ≠ 0, we apply division lemma to 59 and 133, to get

133 = 59 x 2 + 15

Step 3: We consider the new divisor 59 and the new remainder 15, and apply the division lemma to get

59 = 15 x 3 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 990 and 133 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(59,15) = HCF(133,59) = HCF(990,133) .

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Frequently Asked Questions on HCF of 990, 133 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 990, 133?

Answer: HCF of 990, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 990, 133 using Euclid's Algorithm?

Answer: For arbitrary numbers 990, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.