Highest Common Factor of 140, 9749 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 140, 9749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 140, 9749 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 140, 9749 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 140, 9749 is 1.
HCF(140, 9749) = 1
HCF of 140, 9749 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 140, 9749 is 1.
Highest Common Factor of 140,9749 is 1
Step 1: Since 9749 > 140, we apply the division lemma to 9749 and 140, to get
9749 = 140 x 69 + 89
Step 2: Since the reminder 140 ≠ 0, we apply division lemma to 89 and 140, to get
140 = 89 x 1 + 51
Step 3: We consider the new divisor 89 and the new remainder 51, and apply the division lemma to get
89 = 51 x 1 + 38
We consider the new divisor 51 and the new remainder 38,and apply the division lemma to get
51 = 38 x 1 + 13
We consider the new divisor 38 and the new remainder 13,and apply the division lemma to get
38 = 13 x 2 + 12
We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 140 and 9749 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(38,13) = HCF(51,38) = HCF(89,51) = HCF(140,89) = HCF(9749,140) .
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Frequently Asked Questions on HCF of 140, 9749 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 140, 9749?
Answer: HCF of 140, 9749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 140, 9749 using Euclid's Algorithm?
Answer: For arbitrary numbers 140, 9749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.