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 990, 8820, 3891 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 8820, 3891 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 990, 8820, 3891 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 990, 8820, 3891 is 3.
HCF(990, 8820, 3891) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 990, 8820, 3891 is 3.
Step 1: Since 8820 > 990, we apply the division lemma to 8820 and 990, to get
8820 = 990 x 8 + 900
Step 2: Since the reminder 990 ≠ 0, we apply division lemma to 900 and 990, to get
990 = 900 x 1 + 90
Step 3: We consider the new divisor 900 and the new remainder 90, and apply the division lemma to get
900 = 90 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 90, the HCF of 990 and 8820 is 90
Notice that 90 = HCF(900,90) = HCF(990,900) = HCF(8820,990) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3891 > 90, we apply the division lemma to 3891 and 90, to get
3891 = 90 x 43 + 21
Step 2: Since the reminder 90 ≠ 0, we apply division lemma to 21 and 90, to get
90 = 21 x 4 + 6
Step 3: We consider the new divisor 21 and the new remainder 6, and apply the division lemma to get
21 = 6 x 3 + 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 90 and 3891 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(90,21) = HCF(3891,90) .
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 990, 8820, 3891?
Answer: HCF of 990, 8820, 3891 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 8820, 3891 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 8820, 3891 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.