Highest Common Factor of 988, 36140 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, 36140 i.e. 52 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 36140 is 52 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, 36140 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, 36140 is 52.
HCF(988, 36140) = 52
HCF of 988, 36140 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, 36140 is 52.
Highest Common Factor of 988,36140 is 52
Step 1: Since 36140 > 988, we apply the division lemma to 36140 and 988, to get
36140 = 988 x 36 + 572
Step 2: Since the reminder 988 ≠ 0, we apply division lemma to 572 and 988, to get
988 = 572 x 1 + 416
Step 3: We consider the new divisor 572 and the new remainder 416, and apply the division lemma to get
572 = 416 x 1 + 156
We consider the new divisor 416 and the new remainder 156,and apply the division lemma to get
416 = 156 x 2 + 104
We consider the new divisor 156 and the new remainder 104,and apply the division lemma to get
156 = 104 x 1 + 52
We consider the new divisor 104 and the new remainder 52,and apply the division lemma to get
104 = 52 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 988 and 36140 is 52
Notice that 52 = HCF(104,52) = HCF(156,104) = HCF(416,156) = HCF(572,416) = HCF(988,572) = HCF(36140,988) .
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Frequently Asked Questions on HCF of 988, 36140 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, 36140?
Answer: HCF of 988, 36140 is 52 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 36140 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 36140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.