Highest Common Factor of 8582, 7742, 16600 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 8582, 7742, 16600 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8582, 7742, 16600 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 8582, 7742, 16600 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 8582, 7742, 16600 is 2.
HCF(8582, 7742, 16600) = 2
HCF of 8582, 7742, 16600 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8582, 7742, 16600 is 2.
Highest Common Factor of 8582,7742,16600 is 2
Step 1: Since 8582 > 7742, we apply the division lemma to 8582 and 7742, to get
8582 = 7742 x 1 + 840
Step 2: Since the reminder 7742 ≠ 0, we apply division lemma to 840 and 7742, to get
7742 = 840 x 9 + 182
Step 3: We consider the new divisor 840 and the new remainder 182, and apply the division lemma to get
840 = 182 x 4 + 112
We consider the new divisor 182 and the new remainder 112,and apply the division lemma to get
182 = 112 x 1 + 70
We consider the new divisor 112 and the new remainder 70,and apply the division lemma to get
112 = 70 x 1 + 42
We consider the new divisor 70 and the new remainder 42,and apply the division lemma to get
70 = 42 x 1 + 28
We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get
42 = 28 x 1 + 14
We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get
28 = 14 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 8582 and 7742 is 14
Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(70,42) = HCF(112,70) = HCF(182,112) = HCF(840,182) = HCF(7742,840) = HCF(8582,7742) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16600 > 14, we apply the division lemma to 16600 and 14, to get
16600 = 14 x 1185 + 10
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get
14 = 10 x 1 + 4
Step 3: We consider the new divisor 10 and the new remainder 4, and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 16600 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(16600,14) .
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Frequently Asked Questions on HCF of 8582, 7742, 16600 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 8582, 7742, 16600?
Answer: HCF of 8582, 7742, 16600 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8582, 7742, 16600 using Euclid's Algorithm?
Answer: For arbitrary numbers 8582, 7742, 16600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.