Highest Common Factor of 172, 302 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 172, 302 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 172, 302 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 172, 302 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 172, 302 is 2.
HCF(172, 302) = 2
HCF of 172, 302 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 172, 302 is 2.
Highest Common Factor of 172,302 is 2
Step 1: Since 302 > 172, we apply the division lemma to 302 and 172, to get
302 = 172 x 1 + 130
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 130 and 172, to get
172 = 130 x 1 + 42
Step 3: We consider the new divisor 130 and the new remainder 42, and apply the division lemma to get
130 = 42 x 3 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 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 172 and 302 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(130,42) = HCF(172,130) = HCF(302,172) .
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Frequently Asked Questions on HCF of 172, 302 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 172, 302?
Answer: HCF of 172, 302 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 172, 302 using Euclid's Algorithm?
Answer: For arbitrary numbers 172, 302 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.