Highest Common Factor of 182, 2119 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 182, 2119 i.e. 13 the largest integer that leaves a remainder zero for all numbers.
HCF of 182, 2119 is 13 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 182, 2119 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 182, 2119 is 13.
HCF(182, 2119) = 13
HCF of 182, 2119 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 182, 2119 is 13.
Highest Common Factor of 182,2119 is 13
Step 1: Since 2119 > 182, we apply the division lemma to 2119 and 182, to get
2119 = 182 x 11 + 117
Step 2: Since the reminder 182 ≠ 0, we apply division lemma to 117 and 182, to get
182 = 117 x 1 + 65
Step 3: We consider the new divisor 117 and the new remainder 65, and apply the division lemma to get
117 = 65 x 1 + 52
We consider the new divisor 65 and the new remainder 52,and apply the division lemma to get
65 = 52 x 1 + 13
We consider the new divisor 52 and the new remainder 13,and apply the division lemma to get
52 = 13 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 182 and 2119 is 13
Notice that 13 = HCF(52,13) = HCF(65,52) = HCF(117,65) = HCF(182,117) = HCF(2119,182) .
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Frequently Asked Questions on HCF of 182, 2119 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 182, 2119?
Answer: HCF of 182, 2119 is 13 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 182, 2119 using Euclid's Algorithm?
Answer: For arbitrary numbers 182, 2119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.