Highest Common Factor of 988, 1641 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, 1641 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 1641 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 988, 1641 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, 1641 is 1.
HCF(988, 1641) = 1
HCF of 988, 1641 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, 1641 is 1.
Highest Common Factor of 988,1641 is 1
Step 1: Since 1641 > 988, we apply the division lemma to 1641 and 988, to get
1641 = 988 x 1 + 653
Step 2: Since the reminder 988 ≠ 0, we apply division lemma to 653 and 988, to get
988 = 653 x 1 + 335
Step 3: We consider the new divisor 653 and the new remainder 335, and apply the division lemma to get
653 = 335 x 1 + 318
We consider the new divisor 335 and the new remainder 318,and apply the division lemma to get
335 = 318 x 1 + 17
We consider the new divisor 318 and the new remainder 17,and apply the division lemma to get
318 = 17 x 18 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 988 and 1641 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(318,17) = HCF(335,318) = HCF(653,335) = HCF(988,653) = HCF(1641,988) .
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Frequently Asked Questions on HCF of 988, 1641 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, 1641?
Answer: HCF of 988, 1641 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 1641 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 1641 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.