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 6000, 9526, 27118 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6000, 9526, 27118 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 6000, 9526, 27118 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 6000, 9526, 27118 is 2.
HCF(6000, 9526, 27118) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6000, 9526, 27118 is 2.
Step 1: Since 9526 > 6000, we apply the division lemma to 9526 and 6000, to get
9526 = 6000 x 1 + 3526
Step 2: Since the reminder 6000 ≠ 0, we apply division lemma to 3526 and 6000, to get
6000 = 3526 x 1 + 2474
Step 3: We consider the new divisor 3526 and the new remainder 2474, and apply the division lemma to get
3526 = 2474 x 1 + 1052
We consider the new divisor 2474 and the new remainder 1052,and apply the division lemma to get
2474 = 1052 x 2 + 370
We consider the new divisor 1052 and the new remainder 370,and apply the division lemma to get
1052 = 370 x 2 + 312
We consider the new divisor 370 and the new remainder 312,and apply the division lemma to get
370 = 312 x 1 + 58
We consider the new divisor 312 and the new remainder 58,and apply the division lemma to get
312 = 58 x 5 + 22
We consider the new divisor 58 and the new remainder 22,and apply the division lemma to get
58 = 22 x 2 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6000 and 9526 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(58,22) = HCF(312,58) = HCF(370,312) = HCF(1052,370) = HCF(2474,1052) = HCF(3526,2474) = HCF(6000,3526) = HCF(9526,6000) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 27118 > 2, we apply the division lemma to 27118 and 2, to get
27118 = 2 x 13559 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 27118 is 2
Notice that 2 = HCF(27118,2) .
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 6000, 9526, 27118?
Answer: HCF of 6000, 9526, 27118 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6000, 9526, 27118 using Euclid's Algorithm?
Answer: For arbitrary numbers 6000, 9526, 27118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.