Highest Common Factor of 199, 702, 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 199, 702, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 199, 702, 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 199, 702, 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 199, 702, 133 is 1.

HCF(199, 702, 133) = 1

HCF of 199, 702, 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 199, 702, 133 is 1.

Highest Common Factor of 199,702,133 using Euclid's algorithm

Highest Common Factor of 199,702,133 is 1

Step 1: Since 702 > 199, we apply the division lemma to 702 and 199, to get

702 = 199 x 3 + 105

Step 2: Since the reminder 199 ≠ 0, we apply division lemma to 105 and 199, to get

199 = 105 x 1 + 94

Step 3: We consider the new divisor 105 and the new remainder 94, and apply the division lemma to get

105 = 94 x 1 + 11

We consider the new divisor 94 and the new remainder 11,and apply the division lemma to get

94 = 11 x 8 + 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 199 and 702 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(94,11) = HCF(105,94) = HCF(199,105) = HCF(702,199) .

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

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

133 = 1 x 133 + 0

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

Notice that 1 = HCF(133,1) .

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Frequently Asked Questions on HCF of 199, 702, 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 199, 702, 133?

Answer: HCF of 199, 702, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 199, 702, 133 using Euclid's Algorithm?

Answer: For arbitrary numbers 199, 702, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.