Highest Common Factor of 260, 8736 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 260, 8736 i.e. 52 the largest integer that leaves a remainder zero for all numbers.
HCF of 260, 8736 is 52 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 260, 8736 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 260, 8736 is 52.
HCF(260, 8736) = 52
HCF of 260, 8736 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 260, 8736 is 52.
Highest Common Factor of 260,8736 is 52
Step 1: Since 8736 > 260, we apply the division lemma to 8736 and 260, to get
8736 = 260 x 33 + 156
Step 2: Since the reminder 260 ≠ 0, we apply division lemma to 156 and 260, to get
260 = 156 x 1 + 104
Step 3: We consider the new divisor 156 and the new remainder 104, and apply the division lemma to get
156 = 104 x 1 + 52
We consider the new divisor 104 and the new remainder 52, and apply the division lemma to get
104 = 52 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 260 and 8736 is 52
Notice that 52 = HCF(104,52) = HCF(156,104) = HCF(260,156) = HCF(8736,260) .
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Frequently Asked Questions on HCF of 260, 8736 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 260, 8736?
Answer: HCF of 260, 8736 is 52 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 260, 8736 using Euclid's Algorithm?
Answer: For arbitrary numbers 260, 8736 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.