Highest Common Factor of 660, 746, 66 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 660, 746, 66 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 746, 66 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 660, 746, 66 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 660, 746, 66 is 2.
HCF(660, 746, 66) = 2
HCF of 660, 746, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 746, 66 is 2.
Highest Common Factor of 660,746,66 is 2
Step 1: Since 746 > 660, we apply the division lemma to 746 and 660, to get
746 = 660 x 1 + 86
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 86 and 660, to get
660 = 86 x 7 + 58
Step 3: We consider the new divisor 86 and the new remainder 58, and apply the division lemma to get
86 = 58 x 1 + 28
We consider the new divisor 58 and the new remainder 28,and apply the division lemma to get
58 = 28 x 2 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 660 and 746 is 2
Notice that 2 = HCF(28,2) = HCF(58,28) = HCF(86,58) = HCF(660,86) = HCF(746,660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 2, we apply the division lemma to 66 and 2, to get
66 = 2 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 66 is 2
Notice that 2 = HCF(66,2) .
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Frequently Asked Questions on HCF of 660, 746, 66 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 660, 746, 66?
Answer: HCF of 660, 746, 66 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 746, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 746, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.