Highest Common Factor of 55, 66, 110 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 55, 66, 110 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 55, 66, 110 is 11 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 55, 66, 110 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 55, 66, 110 is 11.
HCF(55, 66, 110) = 11
HCF of 55, 66, 110 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 55, 66, 110 is 11.
Highest Common Factor of 55,66,110 is 11
Step 1: Since 66 > 55, we apply the division lemma to 66 and 55, to get
66 = 55 x 1 + 11
Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 11 and 55, to get
55 = 11 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 55 and 66 is 11
Notice that 11 = HCF(55,11) = HCF(66,55) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 110 > 11, we apply the division lemma to 110 and 11, to get
110 = 11 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 11 and 110 is 11
Notice that 11 = HCF(110,11) .
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Frequently Asked Questions on HCF of 55, 66, 110 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 55, 66, 110?
Answer: HCF of 55, 66, 110 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 55, 66, 110 using Euclid's Algorithm?
Answer: For arbitrary numbers 55, 66, 110 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.