Highest Common Factor of 165, 1045, 5377 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 165, 1045, 5377 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 165, 1045, 5377 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 165, 1045, 5377 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 165, 1045, 5377 is 1.
HCF(165, 1045, 5377) = 1
HCF of 165, 1045, 5377 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 165, 1045, 5377 is 1.
Highest Common Factor of 165,1045,5377 is 1
Step 1: Since 1045 > 165, we apply the division lemma to 1045 and 165, to get
1045 = 165 x 6 + 55
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 55 and 165, to get
165 = 55 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 55, the HCF of 165 and 1045 is 55
Notice that 55 = HCF(165,55) = HCF(1045,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5377 > 55, we apply the division lemma to 5377 and 55, to get
5377 = 55 x 97 + 42
Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 42 and 55, to get
55 = 42 x 1 + 13
Step 3: We consider the new divisor 42 and the new remainder 13, and apply the division lemma to get
42 = 13 x 3 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 55 and 5377 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(42,13) = HCF(55,42) = HCF(5377,55) .
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Frequently Asked Questions on HCF of 165, 1045, 5377 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 165, 1045, 5377?
Answer: HCF of 165, 1045, 5377 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 165, 1045, 5377 using Euclid's Algorithm?
Answer: For arbitrary numbers 165, 1045, 5377 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.