Highest Common Factor of 1034, 9162 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 1034, 9162 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1034, 9162 is 2 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 1034, 9162 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 1034, 9162 is 2.
HCF(1034, 9162) = 2
HCF of 1034, 9162 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1034, 9162 is 2.
Highest Common Factor of 1034,9162 is 2
Step 1: Since 9162 > 1034, we apply the division lemma to 9162 and 1034, to get
9162 = 1034 x 8 + 890
Step 2: Since the reminder 1034 ≠ 0, we apply division lemma to 890 and 1034, to get
1034 = 890 x 1 + 144
Step 3: We consider the new divisor 890 and the new remainder 144, and apply the division lemma to get
890 = 144 x 6 + 26
We consider the new divisor 144 and the new remainder 26,and apply the division lemma to get
144 = 26 x 5 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1034 and 9162 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(144,26) = HCF(890,144) = HCF(1034,890) = HCF(9162,1034) .
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Frequently Asked Questions on HCF of 1034, 9162 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 1034, 9162?
Answer: HCF of 1034, 9162 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1034, 9162 using Euclid's Algorithm?
Answer: For arbitrary numbers 1034, 9162 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
