Highest Common Factor of 870, 999, 16 using Euclid's algorithm
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 870, 999, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 999, 16 is 1 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 870, 999, 16 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 870, 999, 16 is 1.
HCF(870, 999, 16) = 1
HCF of 870, 999, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 999, 16 is 1.
Highest Common Factor of 870,999,16 is 1
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 870 and 999 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 16 > 3, we apply the division lemma to 16 and 3, to get
16 = 3 x 5 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 16 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) .
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Frequently Asked Questions on HCF of 870, 999, 16 using Euclid's Algorithm
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 870, 999, 16?
Answer: HCF of 870, 999, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 999, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 999, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.