Highest Common Factor of 3512, 8740 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 3512, 8740 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 3512, 8740 is 4 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 3512, 8740 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 3512, 8740 is 4.
HCF(3512, 8740) = 4
HCF of 3512, 8740 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3512, 8740 is 4.
Highest Common Factor of 3512,8740 is 4
Step 1: Since 8740 > 3512, we apply the division lemma to 8740 and 3512, to get
8740 = 3512 x 2 + 1716
Step 2: Since the reminder 3512 ≠ 0, we apply division lemma to 1716 and 3512, to get
3512 = 1716 x 2 + 80
Step 3: We consider the new divisor 1716 and the new remainder 80, and apply the division lemma to get
1716 = 80 x 21 + 36
We consider the new divisor 80 and the new remainder 36,and apply the division lemma to get
80 = 36 x 2 + 8
We consider the new divisor 36 and the new remainder 8,and apply the division lemma to get
36 = 8 x 4 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 3512 and 8740 is 4
Notice that 4 = HCF(8,4) = HCF(36,8) = HCF(80,36) = HCF(1716,80) = HCF(3512,1716) = HCF(8740,3512) .
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Frequently Asked Questions on HCF of 3512, 8740 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 3512, 8740?
Answer: HCF of 3512, 8740 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3512, 8740 using Euclid's Algorithm?
Answer: For arbitrary numbers 3512, 8740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.