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 894, 309, 102 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 894, 309, 102 is 3 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 894, 309, 102 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 894, 309, 102 is 3.
HCF(894, 309, 102) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 894, 309, 102 is 3.
Step 1: Since 894 > 309, we apply the division lemma to 894 and 309, to get
894 = 309 x 2 + 276
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 276 and 309, to get
309 = 276 x 1 + 33
Step 3: We consider the new divisor 276 and the new remainder 33, and apply the division lemma to get
276 = 33 x 8 + 12
We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get
33 = 12 x 2 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 894 and 309 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(276,33) = HCF(309,276) = HCF(894,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 3, we apply the division lemma to 102 and 3, to get
102 = 3 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 102 is 3
Notice that 3 = HCF(102,3) .
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 894, 309, 102?
Answer: HCF of 894, 309, 102 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 894, 309, 102 using Euclid's Algorithm?
Answer: For arbitrary numbers 894, 309, 102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.