Highest Common Factor of 988, 171 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 988, 171 i.e. 19 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 171 is 19 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 988, 171 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 988, 171 is 19.
HCF(988, 171) = 19
HCF of 988, 171 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 988, 171 is 19.
Highest Common Factor of 988,171 is 19
Step 1: Since 988 > 171, we apply the division lemma to 988 and 171, to get
988 = 171 x 5 + 133
Step 2: Since the reminder 171 ≠ 0, we apply division lemma to 133 and 171, to get
171 = 133 x 1 + 38
Step 3: We consider the new divisor 133 and the new remainder 38, and apply the division lemma to get
133 = 38 x 3 + 19
We consider the new divisor 38 and the new remainder 19, and apply the division lemma to get
38 = 19 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 988 and 171 is 19
Notice that 19 = HCF(38,19) = HCF(133,38) = HCF(171,133) = HCF(988,171) .
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Frequently Asked Questions on HCF of 988, 171 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 988, 171?
Answer: HCF of 988, 171 is 19 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 171 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.