Highest Common Factor of 505, 297, 142 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 505, 297, 142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 505, 297, 142 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 505, 297, 142 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 505, 297, 142 is 1.
HCF(505, 297, 142) = 1
HCF of 505, 297, 142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 505, 297, 142 is 1.
Highest Common Factor of 505,297,142 is 1
Step 1: Since 505 > 297, we apply the division lemma to 505 and 297, to get
505 = 297 x 1 + 208
Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 208 and 297, to get
297 = 208 x 1 + 89
Step 3: We consider the new divisor 208 and the new remainder 89, and apply the division lemma to get
208 = 89 x 2 + 30
We consider the new divisor 89 and the new remainder 30,and apply the division lemma to get
89 = 30 x 2 + 29
We consider the new divisor 30 and the new remainder 29,and apply the division lemma to get
30 = 29 x 1 + 1
We consider the new divisor 29 and the new remainder 1,and apply the division lemma to get
29 = 1 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 505 and 297 is 1
Notice that 1 = HCF(29,1) = HCF(30,29) = HCF(89,30) = HCF(208,89) = HCF(297,208) = HCF(505,297) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 142 > 1, we apply the division lemma to 142 and 1, to get
142 = 1 x 142 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 142 is 1
Notice that 1 = HCF(142,1) .
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Frequently Asked Questions on HCF of 505, 297, 142 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 505, 297, 142?
Answer: HCF of 505, 297, 142 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 505, 297, 142 using Euclid's Algorithm?
Answer: For arbitrary numbers 505, 297, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.