Highest Common Factor of 110, 721, 132 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 110, 721, 132 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 110, 721, 132 is 1 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 110, 721, 132 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 110, 721, 132 is 1.
HCF(110, 721, 132) = 1
HCF of 110, 721, 132 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 110, 721, 132 is 1.
Highest Common Factor of 110,721,132 is 1
Step 1: Since 721 > 110, we apply the division lemma to 721 and 110, to get
721 = 110 x 6 + 61
Step 2: Since the reminder 110 ≠ 0, we apply division lemma to 61 and 110, to get
110 = 61 x 1 + 49
Step 3: We consider the new divisor 61 and the new remainder 49, and apply the division lemma to get
61 = 49 x 1 + 12
We consider the new divisor 49 and the new remainder 12,and apply the division lemma to get
49 = 12 x 4 + 1
We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 110 and 721 is 1
Notice that 1 = HCF(12,1) = HCF(49,12) = HCF(61,49) = HCF(110,61) = HCF(721,110) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 132 > 1, we apply the division lemma to 132 and 1, to get
132 = 1 x 132 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 132 is 1
Notice that 1 = HCF(132,1) .
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Frequently Asked Questions on HCF of 110, 721, 132 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 110, 721, 132?
Answer: HCF of 110, 721, 132 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 110, 721, 132 using Euclid's Algorithm?
Answer: For arbitrary numbers 110, 721, 132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.