Highest Common Factor of 7740, 3205 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 7740, 3205 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 7740, 3205 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 7740, 3205 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 7740, 3205 is 5.
HCF(7740, 3205) = 5
HCF of 7740, 3205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7740, 3205 is 5.
Highest Common Factor of 7740,3205 is 5
Step 1: Since 7740 > 3205, we apply the division lemma to 7740 and 3205, to get
7740 = 3205 x 2 + 1330
Step 2: Since the reminder 3205 ≠ 0, we apply division lemma to 1330 and 3205, to get
3205 = 1330 x 2 + 545
Step 3: We consider the new divisor 1330 and the new remainder 545, and apply the division lemma to get
1330 = 545 x 2 + 240
We consider the new divisor 545 and the new remainder 240,and apply the division lemma to get
545 = 240 x 2 + 65
We consider the new divisor 240 and the new remainder 65,and apply the division lemma to get
240 = 65 x 3 + 45
We consider the new divisor 65 and the new remainder 45,and apply the division lemma to get
65 = 45 x 1 + 20
We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get
45 = 20 x 2 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 7740 and 3205 is 5
Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(65,45) = HCF(240,65) = HCF(545,240) = HCF(1330,545) = HCF(3205,1330) = HCF(7740,3205) .
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Frequently Asked Questions on HCF of 7740, 3205 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 7740, 3205?
Answer: HCF of 7740, 3205 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7740, 3205 using Euclid's Algorithm?
Answer: For arbitrary numbers 7740, 3205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
