Highest Common Factor of 89, 107 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 89, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 89, 107 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 89, 107 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 89, 107 is 1.
HCF(89, 107) = 1
HCF of 89, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 89, 107 is 1.
Highest Common Factor of 89,107 is 1
Step 1: Since 107 > 89, we apply the division lemma to 107 and 89, to get
107 = 89 x 1 + 18
Step 2: Since the reminder 89 ≠ 0, we apply division lemma to 18 and 89, to get
89 = 18 x 4 + 17
Step 3: We consider the new divisor 18 and the new remainder 17, and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1, and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 89 and 107 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(89,18) = HCF(107,89) .
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Frequently Asked Questions on HCF of 89, 107 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 89, 107?
Answer: HCF of 89, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 89, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 89, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.