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 364, 682, 846 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 682, 846 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 364, 682, 846 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 364, 682, 846 is 2.
HCF(364, 682, 846) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 682, 846 is 2.
Step 1: Since 682 > 364, we apply the division lemma to 682 and 364, to get
682 = 364 x 1 + 318
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 318 and 364, to get
364 = 318 x 1 + 46
Step 3: We consider the new divisor 318 and the new remainder 46, and apply the division lemma to get
318 = 46 x 6 + 42
We consider the new divisor 46 and the new remainder 42,and apply the division lemma to get
46 = 42 x 1 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 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 364 and 682 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(46,42) = HCF(318,46) = HCF(364,318) = HCF(682,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 846 > 2, we apply the division lemma to 846 and 2, to get
846 = 2 x 423 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 846 is 2
Notice that 2 = HCF(846,2) .
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 364, 682, 846?
Answer: HCF of 364, 682, 846 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 682, 846 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 682, 846 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.