Highest Common Factor of 380, 860, 502 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 380, 860, 502 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 380, 860, 502 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 380, 860, 502 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 380, 860, 502 is 2.
HCF(380, 860, 502) = 2
HCF of 380, 860, 502 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 380, 860, 502 is 2.
Highest Common Factor of 380,860,502 is 2
Step 1: Since 860 > 380, we apply the division lemma to 860 and 380, to get
860 = 380 x 2 + 100
Step 2: Since the reminder 380 ≠ 0, we apply division lemma to 100 and 380, to get
380 = 100 x 3 + 80
Step 3: We consider the new divisor 100 and the new remainder 80, and apply the division lemma to get
100 = 80 x 1 + 20
We consider the new divisor 80 and the new remainder 20, and apply the division lemma to get
80 = 20 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 380 and 860 is 20
Notice that 20 = HCF(80,20) = HCF(100,80) = HCF(380,100) = HCF(860,380) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 502 > 20, we apply the division lemma to 502 and 20, to get
502 = 20 x 25 + 2
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 2 and 20, to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 20 and 502 is 2
Notice that 2 = HCF(20,2) = HCF(502,20) .
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Frequently Asked Questions on HCF of 380, 860, 502 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 380, 860, 502?
Answer: HCF of 380, 860, 502 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 380, 860, 502 using Euclid's Algorithm?
Answer: For arbitrary numbers 380, 860, 502 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.