Highest Common Factor of 168, 657 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 168, 657 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 168, 657 is 3 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 168, 657 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 168, 657 is 3.
HCF(168, 657) = 3
HCF of 168, 657 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 168, 657 is 3.
Highest Common Factor of 168,657 is 3
Step 1: Since 657 > 168, we apply the division lemma to 657 and 168, to get
657 = 168 x 3 + 153
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 153 and 168, to get
168 = 153 x 1 + 15
Step 3: We consider the new divisor 153 and the new remainder 15, and apply the division lemma to get
153 = 15 x 10 + 3
We consider the new divisor 15 and the new remainder 3, and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 168 and 657 is 3
Notice that 3 = HCF(15,3) = HCF(153,15) = HCF(168,153) = HCF(657,168) .
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Frequently Asked Questions on HCF of 168, 657 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 168, 657?
Answer: HCF of 168, 657 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 168, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 168, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.