Highest Common Factor of 66, 178 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 66, 178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 66, 178 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 66, 178 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 66, 178 is 2.
HCF(66, 178) = 2
HCF of 66, 178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 66, 178 is 2.
Highest Common Factor of 66,178 is 2
Step 1: Since 178 > 66, we apply the division lemma to 178 and 66, to get
178 = 66 x 2 + 46
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 46 and 66, to get
66 = 46 x 1 + 20
Step 3: We consider the new divisor 46 and the new remainder 20, and apply the division lemma to get
46 = 20 x 2 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 178 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(46,20) = HCF(66,46) = HCF(178,66) .
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Frequently Asked Questions on HCF of 66, 178 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 66, 178?
Answer: HCF of 66, 178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 66, 178 using Euclid's Algorithm?
Answer: For arbitrary numbers 66, 178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
