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 8296, 6062, 42654 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8296, 6062, 42654 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 8296, 6062, 42654 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 8296, 6062, 42654 is 2.
HCF(8296, 6062, 42654) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8296, 6062, 42654 is 2.
Step 1: Since 8296 > 6062, we apply the division lemma to 8296 and 6062, to get
8296 = 6062 x 1 + 2234
Step 2: Since the reminder 6062 ≠ 0, we apply division lemma to 2234 and 6062, to get
6062 = 2234 x 2 + 1594
Step 3: We consider the new divisor 2234 and the new remainder 1594, and apply the division lemma to get
2234 = 1594 x 1 + 640
We consider the new divisor 1594 and the new remainder 640,and apply the division lemma to get
1594 = 640 x 2 + 314
We consider the new divisor 640 and the new remainder 314,and apply the division lemma to get
640 = 314 x 2 + 12
We consider the new divisor 314 and the new remainder 12,and apply the division lemma to get
314 = 12 x 26 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8296 and 6062 is 2
Notice that 2 = HCF(12,2) = HCF(314,12) = HCF(640,314) = HCF(1594,640) = HCF(2234,1594) = HCF(6062,2234) = HCF(8296,6062) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42654 > 2, we apply the division lemma to 42654 and 2, to get
42654 = 2 x 21327 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 42654 is 2
Notice that 2 = HCF(42654,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 8296, 6062, 42654?
Answer: HCF of 8296, 6062, 42654 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8296, 6062, 42654 using Euclid's Algorithm?
Answer: For arbitrary numbers 8296, 6062, 42654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.