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 999, 870, 999 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 999, 870, 999 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 999, 870, 999 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 999, 870, 999 is 3.
HCF(999, 870, 999) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 999, 870, 999 is 3.
Step 1: Since 999 > 870, we apply the division lemma to 999 and 870, to get
999 = 870 x 1 + 129
Step 2: Since the reminder 870 ≠ 0, we apply division lemma to 129 and 870, to get
870 = 129 x 6 + 96
Step 3: We consider the new divisor 129 and the new remainder 96, and apply the division lemma to get
129 = 96 x 1 + 33
We consider the new divisor 96 and the new remainder 33,and apply the division lemma to get
96 = 33 x 2 + 30
We consider the new divisor 33 and the new remainder 30,and apply the division lemma to get
33 = 30 x 1 + 3
We consider the new divisor 30 and the new remainder 3,and apply the division lemma to get
30 = 3 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 999 and 870 is 3
Notice that 3 = HCF(30,3) = HCF(33,30) = HCF(96,33) = HCF(129,96) = HCF(870,129) = HCF(999,870) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 999 > 3, we apply the division lemma to 999 and 3, to get
999 = 3 x 333 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 999 is 3
Notice that 3 = HCF(999,3) .
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 999, 870, 999?
Answer: HCF of 999, 870, 999 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 999, 870, 999 using Euclid's Algorithm?
Answer: For arbitrary numbers 999, 870, 999 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.