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 459, 840 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 459, 840 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 459, 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 459, 840 is 3.
HCF(459, 840) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 459, 840 is 3.
Step 1: Since 840 > 459, we apply the division lemma to 840 and 459, to get
840 = 459 x 1 + 381
Step 2: Since the reminder 459 ≠ 0, we apply division lemma to 381 and 459, to get
459 = 381 x 1 + 78
Step 3: We consider the new divisor 381 and the new remainder 78, and apply the division lemma to get
381 = 78 x 4 + 69
We consider the new divisor 78 and the new remainder 69,and apply the division lemma to get
78 = 69 x 1 + 9
We consider the new divisor 69 and the new remainder 9,and apply the division lemma to get
69 = 9 x 7 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 459 and 840 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(69,9) = HCF(78,69) = HCF(381,78) = HCF(459,381) = HCF(840,459) .
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 459, 840?
Answer: HCF of 459, 840 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 459, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 459, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.