Highest Common Factor of 32, 117 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 32, 117 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 32, 117 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 32, 117 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 32, 117 is 1.
HCF(32, 117) = 1
HCF of 32, 117 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 32, 117 is 1.
Highest Common Factor of 32,117 is 1
Step 1: Since 117 > 32, we apply the division lemma to 117 and 32, to get
117 = 32 x 3 + 21
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 21 and 32, to get
32 = 21 x 1 + 11
Step 3: We consider the new divisor 21 and the new remainder 11, and apply the division lemma to get
21 = 11 x 1 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 32 and 117 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(117,32) .
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Frequently Asked Questions on HCF of 32, 117 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 32, 117?
Answer: HCF of 32, 117 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 32, 117 using Euclid's Algorithm?
Answer: For arbitrary numbers 32, 117 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.