Highest Common Factor of 985, 9975, 5101 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 985, 9975, 5101 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 985, 9975, 5101 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 985, 9975, 5101 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 985, 9975, 5101 is 1.
HCF(985, 9975, 5101) = 1
HCF of 985, 9975, 5101 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 985, 9975, 5101 is 1.
Highest Common Factor of 985,9975,5101 is 1
Step 1: Since 9975 > 985, we apply the division lemma to 9975 and 985, to get
9975 = 985 x 10 + 125
Step 2: Since the reminder 985 ≠ 0, we apply division lemma to 125 and 985, to get
985 = 125 x 7 + 110
Step 3: We consider the new divisor 125 and the new remainder 110, and apply the division lemma to get
125 = 110 x 1 + 15
We consider the new divisor 110 and the new remainder 15,and apply the division lemma to get
110 = 15 x 7 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 985 and 9975 is 5
Notice that 5 = HCF(15,5) = HCF(110,15) = HCF(125,110) = HCF(985,125) = HCF(9975,985) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5101 > 5, we apply the division lemma to 5101 and 5, to get
5101 = 5 x 1020 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 5101 is 1
Notice that 1 = HCF(5,1) = HCF(5101,5) .
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Frequently Asked Questions on HCF of 985, 9975, 5101 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 985, 9975, 5101?
Answer: HCF of 985, 9975, 5101 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 985, 9975, 5101 using Euclid's Algorithm?
Answer: For arbitrary numbers 985, 9975, 5101 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.