Highest Common Factor of 132, 77 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, 77 i.e. 11 the largest integer that leaves a remainder zero for all numbers.
HCF of 132, 77 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 132, 77 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, 77 is 11.
HCF(132, 77) = 11
HCF of 132, 77 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, 77 is 11.
Highest Common Factor of 132,77 is 11
Step 1: Since 132 > 77, we apply the division lemma to 132 and 77, to get
132 = 77 x 1 + 55
Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 55 and 77, to get
77 = 55 x 1 + 22
Step 3: We consider the new divisor 55 and the new remainder 22, and apply the division lemma to get
55 = 22 x 2 + 11
We consider the new divisor 22 and the new remainder 11, and apply the division lemma to get
22 = 11 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 132 and 77 is 11
Notice that 11 = HCF(22,11) = HCF(55,22) = HCF(77,55) = HCF(132,77) .
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Frequently Asked Questions on HCF of 132, 77 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, 77?
Answer: HCF of 132, 77 is 11 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 132, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 132, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.