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 774, 8182 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 8182 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 774, 8182 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 774, 8182 is 2.
HCF(774, 8182) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 8182 is 2.
Step 1: Since 8182 > 774, we apply the division lemma to 8182 and 774, to get
8182 = 774 x 10 + 442
Step 2: Since the reminder 774 ≠ 0, we apply division lemma to 442 and 774, to get
774 = 442 x 1 + 332
Step 3: We consider the new divisor 442 and the new remainder 332, and apply the division lemma to get
442 = 332 x 1 + 110
We consider the new divisor 332 and the new remainder 110,and apply the division lemma to get
332 = 110 x 3 + 2
We consider the new divisor 110 and the new remainder 2,and apply the division lemma to get
110 = 2 x 55 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 774 and 8182 is 2
Notice that 2 = HCF(110,2) = HCF(332,110) = HCF(442,332) = HCF(774,442) = HCF(8182,774) .
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 774, 8182?
Answer: HCF of 774, 8182 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 8182 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 8182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.