Highest Common Factor of 132, 912, 731 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 132, 912, 731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 132, 912, 731 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 132, 912, 731 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 132, 912, 731 is 1.
HCF(132, 912, 731) = 1
HCF of 132, 912, 731 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 132, 912, 731 is 1.
Highest Common Factor of 132,912,731 is 1
Step 1: Since 912 > 132, we apply the division lemma to 912 and 132, to get
912 = 132 x 6 + 120
Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 120 and 132, to get
132 = 120 x 1 + 12
Step 3: We consider the new divisor 120 and the new remainder 12, and apply the division lemma to get
120 = 12 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 132 and 912 is 12
Notice that 12 = HCF(120,12) = HCF(132,120) = HCF(912,132) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 731 > 12, we apply the division lemma to 731 and 12, to get
731 = 12 x 60 + 11
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 11 and 12, to get
12 = 11 x 1 + 1
Step 3: We consider the new divisor 11 and the new remainder 1, and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 12 and 731 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(731,12) .
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Frequently Asked Questions on HCF of 132, 912, 731 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 132, 912, 731?
Answer: HCF of 132, 912, 731 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 132, 912, 731 using Euclid's Algorithm?
Answer: For arbitrary numbers 132, 912, 731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.