Highest Common Factor of 1642, 7942, 82616 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 1642, 7942, 82616 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1642, 7942, 82616 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 1642, 7942, 82616 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 1642, 7942, 82616 is 2.
HCF(1642, 7942, 82616) = 2
HCF of 1642, 7942, 82616 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1642, 7942, 82616 is 2.
Highest Common Factor of 1642,7942,82616 is 2
Step 1: Since 7942 > 1642, we apply the division lemma to 7942 and 1642, to get
7942 = 1642 x 4 + 1374
Step 2: Since the reminder 1642 ≠ 0, we apply division lemma to 1374 and 1642, to get
1642 = 1374 x 1 + 268
Step 3: We consider the new divisor 1374 and the new remainder 268, and apply the division lemma to get
1374 = 268 x 5 + 34
We consider the new divisor 268 and the new remainder 34,and apply the division lemma to get
268 = 34 x 7 + 30
We consider the new divisor 34 and the new remainder 30,and apply the division lemma to get
34 = 30 x 1 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1642 and 7942 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(34,30) = HCF(268,34) = HCF(1374,268) = HCF(1642,1374) = HCF(7942,1642) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82616 > 2, we apply the division lemma to 82616 and 2, to get
82616 = 2 x 41308 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 82616 is 2
Notice that 2 = HCF(82616,2) .
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Frequently Asked Questions on HCF of 1642, 7942, 82616 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 1642, 7942, 82616?
Answer: HCF of 1642, 7942, 82616 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1642, 7942, 82616 using Euclid's Algorithm?
Answer: For arbitrary numbers 1642, 7942, 82616 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.