Highest Common Factor of 502, 868, 185 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, 868, 185 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 502, 868, 185 is 1 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, 868, 185 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, 868, 185 is 1.
HCF(502, 868, 185) = 1
HCF of 502, 868, 185 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, 868, 185 is 1.
Highest Common Factor of 502,868,185 is 1
Step 1: Since 868 > 502, we apply the division lemma to 868 and 502, to get
868 = 502 x 1 + 366
Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 366 and 502, to get
502 = 366 x 1 + 136
Step 3: We consider the new divisor 366 and the new remainder 136, and apply the division lemma to get
366 = 136 x 2 + 94
We consider the new divisor 136 and the new remainder 94,and apply the division lemma to get
136 = 94 x 1 + 42
We consider the new divisor 94 and the new remainder 42,and apply the division lemma to get
94 = 42 x 2 + 10
We consider the new divisor 42 and the new remainder 10,and apply the division lemma to get
42 = 10 x 4 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 502 and 868 is 2
Notice that 2 = HCF(10,2) = HCF(42,10) = HCF(94,42) = HCF(136,94) = HCF(366,136) = HCF(502,366) = HCF(868,502) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 185 > 2, we apply the division lemma to 185 and 2, to get
185 = 2 x 92 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 185 is 1
Notice that 1 = HCF(2,1) = HCF(185,2) .
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Frequently Asked Questions on HCF of 502, 868, 185 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, 868, 185?
Answer: HCF of 502, 868, 185 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 502, 868, 185 using Euclid's Algorithm?
Answer: For arbitrary numbers 502, 868, 185 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.