Highest Common Factor of 109, 68, 514, 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 109, 68, 514, 502 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 109, 68, 514, 502 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 109, 68, 514, 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 109, 68, 514, 502 is 1.
HCF(109, 68, 514, 502) = 1
HCF of 109, 68, 514, 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 109, 68, 514, 502 is 1.
Highest Common Factor of 109,68,514,502 is 1
Step 1: Since 109 > 68, we apply the division lemma to 109 and 68, to get
109 = 68 x 1 + 41
Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 41 and 68, to get
68 = 41 x 1 + 27
Step 3: We consider the new divisor 41 and the new remainder 27, and apply the division lemma to get
41 = 27 x 1 + 14
We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get
27 = 14 x 1 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 109 and 68 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(41,27) = HCF(68,41) = HCF(109,68) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 1, we apply the division lemma to 514 and 1, to get
514 = 1 x 514 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 514 is 1
Notice that 1 = HCF(514,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 502 > 1, we apply the division lemma to 502 and 1, to get
502 = 1 x 502 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 502 is 1
Notice that 1 = HCF(502,1) .
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Frequently Asked Questions on HCF of 109, 68, 514, 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 109, 68, 514, 502?
Answer: HCF of 109, 68, 514, 502 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 109, 68, 514, 502 using Euclid's Algorithm?
Answer: For arbitrary numbers 109, 68, 514, 502 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.