Highest Common Factor of 105, 495, 160 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 105, 495, 160 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 495, 160 is 5 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 105, 495, 160 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 105, 495, 160 is 5.
HCF(105, 495, 160) = 5
HCF of 105, 495, 160 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 105, 495, 160 is 5.
Highest Common Factor of 105,495,160 is 5
Step 1: Since 495 > 105, we apply the division lemma to 495 and 105, to get
495 = 105 x 4 + 75
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 75 and 105, to get
105 = 75 x 1 + 30
Step 3: We consider the new divisor 75 and the new remainder 30, and apply the division lemma to get
75 = 30 x 2 + 15
We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 105 and 495 is 15
Notice that 15 = HCF(30,15) = HCF(75,30) = HCF(105,75) = HCF(495,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 160 > 15, we apply the division lemma to 160 and 15, to get
160 = 15 x 10 + 10
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 10 and 15, to get
15 = 10 x 1 + 5
Step 3: We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 15 and 160 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(160,15) .
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Frequently Asked Questions on HCF of 105, 495, 160 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 105, 495, 160?
Answer: HCF of 105, 495, 160 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 495, 160 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 495, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.