Highest Common Factor of 66, 116, 706 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, 116, 706 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 66, 116, 706 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, 116, 706 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, 116, 706 is 2.
HCF(66, 116, 706) = 2
HCF of 66, 116, 706 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, 116, 706 is 2.
Highest Common Factor of 66,116,706 is 2
Step 1: Since 116 > 66, we apply the division lemma to 116 and 66, to get
116 = 66 x 1 + 50
Step 2: Since the reminder 66 ≠ 0, we apply division lemma to 50 and 66, to get
66 = 50 x 1 + 16
Step 3: We consider the new divisor 50 and the new remainder 16, and apply the division lemma to get
50 = 16 x 3 + 2
We consider the new divisor 16 and the new remainder 2, and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 116 is 2
Notice that 2 = HCF(16,2) = HCF(50,16) = HCF(66,50) = HCF(116,66) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 706 > 2, we apply the division lemma to 706 and 2, to get
706 = 2 x 353 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 706 is 2
Notice that 2 = HCF(706,2) .
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Frequently Asked Questions on HCF of 66, 116, 706 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, 116, 706?
Answer: HCF of 66, 116, 706 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 66, 116, 706 using Euclid's Algorithm?
Answer: For arbitrary numbers 66, 116, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.