Highest Common Factor of 8680, 9735 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 8680, 9735 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 8680, 9735 is 5 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 8680, 9735 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 8680, 9735 is 5.
HCF(8680, 9735) = 5
HCF of 8680, 9735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8680, 9735 is 5.
Highest Common Factor of 8680,9735 is 5
Step 1: Since 9735 > 8680, we apply the division lemma to 9735 and 8680, to get
9735 = 8680 x 1 + 1055
Step 2: Since the reminder 8680 ≠ 0, we apply division lemma to 1055 and 8680, to get
8680 = 1055 x 8 + 240
Step 3: We consider the new divisor 1055 and the new remainder 240, and apply the division lemma to get
1055 = 240 x 4 + 95
We consider the new divisor 240 and the new remainder 95,and apply the division lemma to get
240 = 95 x 2 + 50
We consider the new divisor 95 and the new remainder 50,and apply the division lemma to get
95 = 50 x 1 + 45
We consider the new divisor 50 and the new remainder 45,and apply the division lemma to get
50 = 45 x 1 + 5
We consider the new divisor 45 and the new remainder 5,and apply the division lemma to get
45 = 5 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 8680 and 9735 is 5
Notice that 5 = HCF(45,5) = HCF(50,45) = HCF(95,50) = HCF(240,95) = HCF(1055,240) = HCF(8680,1055) = HCF(9735,8680) .
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Frequently Asked Questions on HCF of 8680, 9735 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 8680, 9735?
Answer: HCF of 8680, 9735 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8680, 9735 using Euclid's Algorithm?
Answer: For arbitrary numbers 8680, 9735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.