Highest Common Factor of 502, 142 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, 142 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 502, 142 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, 142 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, 142 is 2.
HCF(502, 142) = 2
HCF of 502, 142 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, 142 is 2.
Highest Common Factor of 502,142 is 2
Step 1: Since 502 > 142, we apply the division lemma to 502 and 142, to get
502 = 142 x 3 + 76
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 76 and 142, to get
142 = 76 x 1 + 66
Step 3: We consider the new divisor 76 and the new remainder 66, and apply the division lemma to get
76 = 66 x 1 + 10
We consider the new divisor 66 and the new remainder 10,and apply the division lemma to get
66 = 10 x 6 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 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 142 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(66,10) = HCF(76,66) = HCF(142,76) = HCF(502,142) .
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Frequently Asked Questions on HCF of 502, 142 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, 142?
Answer: HCF of 502, 142 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 502, 142 using Euclid's Algorithm?
Answer: For arbitrary numbers 502, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.