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 7096, 6228, 97794 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7096, 6228, 97794 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 7096, 6228, 97794 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 7096, 6228, 97794 is 2.
HCF(7096, 6228, 97794) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7096, 6228, 97794 is 2.
Step 1: Since 7096 > 6228, we apply the division lemma to 7096 and 6228, to get
7096 = 6228 x 1 + 868
Step 2: Since the reminder 6228 ≠ 0, we apply division lemma to 868 and 6228, to get
6228 = 868 x 7 + 152
Step 3: We consider the new divisor 868 and the new remainder 152, and apply the division lemma to get
868 = 152 x 5 + 108
We consider the new divisor 152 and the new remainder 108,and apply the division lemma to get
152 = 108 x 1 + 44
We consider the new divisor 108 and the new remainder 44,and apply the division lemma to get
108 = 44 x 2 + 20
We consider the new divisor 44 and the new remainder 20,and apply the division lemma to get
44 = 20 x 2 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 7096 and 6228 is 4
Notice that 4 = HCF(20,4) = HCF(44,20) = HCF(108,44) = HCF(152,108) = HCF(868,152) = HCF(6228,868) = HCF(7096,6228) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 97794 > 4, we apply the division lemma to 97794 and 4, to get
97794 = 4 x 24448 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 97794 is 2
Notice that 2 = HCF(4,2) = HCF(97794,4) .
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 7096, 6228, 97794?
Answer: HCF of 7096, 6228, 97794 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7096, 6228, 97794 using Euclid's Algorithm?
Answer: For arbitrary numbers 7096, 6228, 97794 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.