Highest Common Factor of 502, 342, 114 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 502, 342, 114 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 502, 342, 114 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 502, 342, 114 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 502, 342, 114 is 2.
HCF(502, 342, 114) = 2
HCF of 502, 342, 114 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 502, 342, 114 is 2.
Highest Common Factor of 502,342,114 is 2
Step 1: Since 502 > 342, we apply the division lemma to 502 and 342, to get
502 = 342 x 1 + 160
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 160 and 342, to get
342 = 160 x 2 + 22
Step 3: We consider the new divisor 160 and the new remainder 22, and apply the division lemma to get
160 = 22 x 7 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 502 and 342 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(160,22) = HCF(342,160) = HCF(502,342) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 2, we apply the division lemma to 114 and 2, to get
114 = 2 x 57 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 114 is 2
Notice that 2 = HCF(114,2) .
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Frequently Asked Questions on HCF of 502, 342, 114 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 502, 342, 114?
Answer: HCF of 502, 342, 114 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 502, 342, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 502, 342, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.