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 800, 514, 840 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 514, 840 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 800, 514, 840 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 800, 514, 840 is 2.
HCF(800, 514, 840) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 800, 514, 840 is 2.
Step 1: Since 800 > 514, we apply the division lemma to 800 and 514, to get
800 = 514 x 1 + 286
Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 286 and 514, to get
514 = 286 x 1 + 228
Step 3: We consider the new divisor 286 and the new remainder 228, and apply the division lemma to get
286 = 228 x 1 + 58
We consider the new divisor 228 and the new remainder 58,and apply the division lemma to get
228 = 58 x 3 + 54
We consider the new divisor 58 and the new remainder 54,and apply the division lemma to get
58 = 54 x 1 + 4
We consider the new divisor 54 and the new remainder 4,and apply the division lemma to get
54 = 4 x 13 + 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 800 and 514 is 2
Notice that 2 = HCF(4,2) = HCF(54,4) = HCF(58,54) = HCF(228,58) = HCF(286,228) = HCF(514,286) = HCF(800,514) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 840 > 2, we apply the division lemma to 840 and 2, to get
840 = 2 x 420 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 840 is 2
Notice that 2 = HCF(840,2) .
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 800, 514, 840?
Answer: HCF of 800, 514, 840 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 514, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 514, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.