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 8992, 6846, 89574 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8992, 6846, 89574 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 8992, 6846, 89574 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 8992, 6846, 89574 is 2.
HCF(8992, 6846, 89574) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8992, 6846, 89574 is 2.
Step 1: Since 8992 > 6846, we apply the division lemma to 8992 and 6846, to get
8992 = 6846 x 1 + 2146
Step 2: Since the reminder 6846 ≠ 0, we apply division lemma to 2146 and 6846, to get
6846 = 2146 x 3 + 408
Step 3: We consider the new divisor 2146 and the new remainder 408, and apply the division lemma to get
2146 = 408 x 5 + 106
We consider the new divisor 408 and the new remainder 106,and apply the division lemma to get
408 = 106 x 3 + 90
We consider the new divisor 106 and the new remainder 90,and apply the division lemma to get
106 = 90 x 1 + 16
We consider the new divisor 90 and the new remainder 16,and apply the division lemma to get
90 = 16 x 5 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 8992 and 6846 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(90,16) = HCF(106,90) = HCF(408,106) = HCF(2146,408) = HCF(6846,2146) = HCF(8992,6846) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 89574 > 2, we apply the division lemma to 89574 and 2, to get
89574 = 2 x 44787 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 89574 is 2
Notice that 2 = HCF(89574,2) .
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 8992, 6846, 89574?
Answer: HCF of 8992, 6846, 89574 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8992, 6846, 89574 using Euclid's Algorithm?
Answer: For arbitrary numbers 8992, 6846, 89574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.