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 5662, 8402, 12845 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5662, 8402, 12845 is 1 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 5662, 8402, 12845 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 5662, 8402, 12845 is 1.
HCF(5662, 8402, 12845) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5662, 8402, 12845 is 1.
Step 1: Since 8402 > 5662, we apply the division lemma to 8402 and 5662, to get
8402 = 5662 x 1 + 2740
Step 2: Since the reminder 5662 ≠ 0, we apply division lemma to 2740 and 5662, to get
5662 = 2740 x 2 + 182
Step 3: We consider the new divisor 2740 and the new remainder 182, and apply the division lemma to get
2740 = 182 x 15 + 10
We consider the new divisor 182 and the new remainder 10,and apply the division lemma to get
182 = 10 x 18 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5662 and 8402 is 2
Notice that 2 = HCF(10,2) = HCF(182,10) = HCF(2740,182) = HCF(5662,2740) = HCF(8402,5662) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12845 > 2, we apply the division lemma to 12845 and 2, to get
12845 = 2 x 6422 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 12845 is 1
Notice that 1 = HCF(2,1) = HCF(12845,2) .
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 5662, 8402, 12845?
Answer: HCF of 5662, 8402, 12845 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5662, 8402, 12845 using Euclid's Algorithm?
Answer: For arbitrary numbers 5662, 8402, 12845 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.