Highest Common Factor of 8435, 8712, 60249 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 8435, 8712, 60249 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8435, 8712, 60249 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 8435, 8712, 60249 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 8435, 8712, 60249 is 1.
HCF(8435, 8712, 60249) = 1
HCF of 8435, 8712, 60249 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8435, 8712, 60249 is 1.
Highest Common Factor of 8435,8712,60249 is 1
Step 1: Since 8712 > 8435, we apply the division lemma to 8712 and 8435, to get
8712 = 8435 x 1 + 277
Step 2: Since the reminder 8435 ≠ 0, we apply division lemma to 277 and 8435, to get
8435 = 277 x 30 + 125
Step 3: We consider the new divisor 277 and the new remainder 125, and apply the division lemma to get
277 = 125 x 2 + 27
We consider the new divisor 125 and the new remainder 27,and apply the division lemma to get
125 = 27 x 4 + 17
We consider the new divisor 27 and the new remainder 17,and apply the division lemma to get
27 = 17 x 1 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8435 and 8712 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(27,17) = HCF(125,27) = HCF(277,125) = HCF(8435,277) = HCF(8712,8435) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60249 > 1, we apply the division lemma to 60249 and 1, to get
60249 = 1 x 60249 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 60249 is 1
Notice that 1 = HCF(60249,1) .
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Frequently Asked Questions on HCF of 8435, 8712, 60249 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 8435, 8712, 60249?
Answer: HCF of 8435, 8712, 60249 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8435, 8712, 60249 using Euclid's Algorithm?
Answer: For arbitrary numbers 8435, 8712, 60249 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.