Highest Common Factor of 870, 997, 664, 14 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, 997, 664, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 997, 664, 14 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, 997, 664, 14 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, 997, 664, 14 is 1.
HCF(870, 997, 664, 14) = 1
HCF of 870, 997, 664, 14 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, 997, 664, 14 is 1.
Highest Common Factor of 870,997,664,14 is 1
Step 1: Since 997 > 870, we apply the division lemma to 997 and 870, to get
997 = 870 x 1 + 127
Step 2: Since the reminder 870 ≠ 0, we apply division lemma to 127 and 870, to get
870 = 127 x 6 + 108
Step 3: We consider the new divisor 127 and the new remainder 108, and apply the division lemma to get
127 = 108 x 1 + 19
We consider the new divisor 108 and the new remainder 19,and apply the division lemma to get
108 = 19 x 5 + 13
We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get
19 = 13 x 1 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 870 and 997 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(108,19) = HCF(127,108) = HCF(870,127) = HCF(997,870) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 664 > 1, we apply the division lemma to 664 and 1, to get
664 = 1 x 664 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 664 is 1
Notice that 1 = HCF(664,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1
Notice that 1 = HCF(14,1) .
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Frequently Asked Questions on HCF of 870, 997, 664, 14 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, 997, 664, 14?
Answer: HCF of 870, 997, 664, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 997, 664, 14 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 997, 664, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.