Highest Common Factor of 7040, 2696, 41082 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 7040, 2696, 41082 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7040, 2696, 41082 is 2 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 7040, 2696, 41082 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 7040, 2696, 41082 is 2.
HCF(7040, 2696, 41082) = 2
HCF of 7040, 2696, 41082 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7040, 2696, 41082 is 2.
Highest Common Factor of 7040,2696,41082 is 2
Step 1: Since 7040 > 2696, we apply the division lemma to 7040 and 2696, to get
7040 = 2696 x 2 + 1648
Step 2: Since the reminder 2696 ≠ 0, we apply division lemma to 1648 and 2696, to get
2696 = 1648 x 1 + 1048
Step 3: We consider the new divisor 1648 and the new remainder 1048, and apply the division lemma to get
1648 = 1048 x 1 + 600
We consider the new divisor 1048 and the new remainder 600,and apply the division lemma to get
1048 = 600 x 1 + 448
We consider the new divisor 600 and the new remainder 448,and apply the division lemma to get
600 = 448 x 1 + 152
We consider the new divisor 448 and the new remainder 152,and apply the division lemma to get
448 = 152 x 2 + 144
We consider the new divisor 152 and the new remainder 144,and apply the division lemma to get
152 = 144 x 1 + 8
We consider the new divisor 144 and the new remainder 8,and apply the division lemma to get
144 = 8 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 7040 and 2696 is 8
Notice that 8 = HCF(144,8) = HCF(152,144) = HCF(448,152) = HCF(600,448) = HCF(1048,600) = HCF(1648,1048) = HCF(2696,1648) = HCF(7040,2696) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 41082 > 8, we apply the division lemma to 41082 and 8, to get
41082 = 8 x 5135 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 41082 is 2
Notice that 2 = HCF(8,2) = HCF(41082,8) .
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Frequently Asked Questions on HCF of 7040, 2696, 41082 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 7040, 2696, 41082?
Answer: HCF of 7040, 2696, 41082 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7040, 2696, 41082 using Euclid's Algorithm?
Answer: For arbitrary numbers 7040, 2696, 41082 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.