Highest Common Factor of 7162, 984 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 7162, 984 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7162, 984 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 7162, 984 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 7162, 984 is 2.
HCF(7162, 984) = 2
HCF of 7162, 984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7162, 984 is 2.
Highest Common Factor of 7162,984 is 2
Step 1: Since 7162 > 984, we apply the division lemma to 7162 and 984, to get
7162 = 984 x 7 + 274
Step 2: Since the reminder 984 ≠ 0, we apply division lemma to 274 and 984, to get
984 = 274 x 3 + 162
Step 3: We consider the new divisor 274 and the new remainder 162, and apply the division lemma to get
274 = 162 x 1 + 112
We consider the new divisor 162 and the new remainder 112,and apply the division lemma to get
162 = 112 x 1 + 50
We consider the new divisor 112 and the new remainder 50,and apply the division lemma to get
112 = 50 x 2 + 12
We consider the new divisor 50 and the new remainder 12,and apply the division lemma to get
50 = 12 x 4 + 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 7162 and 984 is 2
Notice that 2 = HCF(12,2) = HCF(50,12) = HCF(112,50) = HCF(162,112) = HCF(274,162) = HCF(984,274) = HCF(7162,984) .
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Frequently Asked Questions on HCF of 7162, 984 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 7162, 984?
Answer: HCF of 7162, 984 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7162, 984 using Euclid's Algorithm?
Answer: For arbitrary numbers 7162, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.