Highest Common Factor of 160, 34054 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 160, 34054 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 160, 34054 is 2 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 160, 34054 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 160, 34054 is 2.
HCF(160, 34054) = 2
HCF of 160, 34054 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 160, 34054 is 2.
Highest Common Factor of 160,34054 is 2
Step 1: Since 34054 > 160, we apply the division lemma to 34054 and 160, to get
34054 = 160 x 212 + 134
Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 134 and 160, to get
160 = 134 x 1 + 26
Step 3: We consider the new divisor 134 and the new remainder 26, and apply the division lemma to get
134 = 26 x 5 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 160 and 34054 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(134,26) = HCF(160,134) = HCF(34054,160) .
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Frequently Asked Questions on HCF of 160, 34054 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 160, 34054?
Answer: HCF of 160, 34054 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 160, 34054 using Euclid's Algorithm?
Answer: For arbitrary numbers 160, 34054 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
