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 846, 288, 824 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 846, 288, 824 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 846, 288, 824 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 846, 288, 824 is 2.
HCF(846, 288, 824) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 846, 288, 824 is 2.
Step 1: Since 846 > 288, we apply the division lemma to 846 and 288, to get
846 = 288 x 2 + 270
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 270 and 288, to get
288 = 270 x 1 + 18
Step 3: We consider the new divisor 270 and the new remainder 18, and apply the division lemma to get
270 = 18 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 846 and 288 is 18
Notice that 18 = HCF(270,18) = HCF(288,270) = HCF(846,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 824 > 18, we apply the division lemma to 824 and 18, to get
824 = 18 x 45 + 14
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 14 and 18, to get
18 = 14 x 1 + 4
Step 3: We consider the new divisor 14 and the new remainder 4, and apply the division lemma to get
14 = 4 x 3 + 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 18 and 824 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(824,18) .
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 846, 288, 824?
Answer: HCF of 846, 288, 824 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 846, 288, 824 using Euclid's Algorithm?
Answer: For arbitrary numbers 846, 288, 824 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.