Highest Common Factor of 9968, 8140 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 9968, 8140 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 9968, 8140 is 4 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 9968, 8140 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 9968, 8140 is 4.
HCF(9968, 8140) = 4
HCF of 9968, 8140 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9968, 8140 is 4.
Highest Common Factor of 9968,8140 is 4
Step 1: Since 9968 > 8140, we apply the division lemma to 9968 and 8140, to get
9968 = 8140 x 1 + 1828
Step 2: Since the reminder 8140 ≠ 0, we apply division lemma to 1828 and 8140, to get
8140 = 1828 x 4 + 828
Step 3: We consider the new divisor 1828 and the new remainder 828, and apply the division lemma to get
1828 = 828 x 2 + 172
We consider the new divisor 828 and the new remainder 172,and apply the division lemma to get
828 = 172 x 4 + 140
We consider the new divisor 172 and the new remainder 140,and apply the division lemma to get
172 = 140 x 1 + 32
We consider the new divisor 140 and the new remainder 32,and apply the division lemma to get
140 = 32 x 4 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 9968 and 8140 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(140,32) = HCF(172,140) = HCF(828,172) = HCF(1828,828) = HCF(8140,1828) = HCF(9968,8140) .
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Frequently Asked Questions on HCF of 9968, 8140 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 9968, 8140?
Answer: HCF of 9968, 8140 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9968, 8140 using Euclid's Algorithm?
Answer: For arbitrary numbers 9968, 8140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
