Highest Common Factor of 170, 30198 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 170, 30198 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 30198 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 170, 30198 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 170, 30198 is 2.
HCF(170, 30198) = 2
HCF of 170, 30198 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 30198 is 2.
Highest Common Factor of 170,30198 is 2
Step 1: Since 30198 > 170, we apply the division lemma to 30198 and 170, to get
30198 = 170 x 177 + 108
Step 2: Since the reminder 170 ≠ 0, we apply division lemma to 108 and 170, to get
170 = 108 x 1 + 62
Step 3: We consider the new divisor 108 and the new remainder 62, and apply the division lemma to get
108 = 62 x 1 + 46
We consider the new divisor 62 and the new remainder 46,and apply the division lemma to get
62 = 46 x 1 + 16
We consider the new divisor 46 and the new remainder 16,and apply the division lemma to get
46 = 16 x 2 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 170 and 30198 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(46,16) = HCF(62,46) = HCF(108,62) = HCF(170,108) = HCF(30198,170) .
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Frequently Asked Questions on HCF of 170, 30198 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 170, 30198?
Answer: HCF of 170, 30198 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 30198 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 30198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
