Highest Common Factor of 357, 7269 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 357, 7269 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 7269 is 3 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 357, 7269 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 357, 7269 is 3.
HCF(357, 7269) = 3
HCF of 357, 7269 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 357, 7269 is 3.
Highest Common Factor of 357,7269 is 3
Step 1: Since 7269 > 357, we apply the division lemma to 7269 and 357, to get
7269 = 357 x 20 + 129
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 129 and 357, to get
357 = 129 x 2 + 99
Step 3: We consider the new divisor 129 and the new remainder 99, and apply the division lemma to get
129 = 99 x 1 + 30
We consider the new divisor 99 and the new remainder 30,and apply the division lemma to get
99 = 30 x 3 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 357 and 7269 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(99,30) = HCF(129,99) = HCF(357,129) = HCF(7269,357) .
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Frequently Asked Questions on HCF of 357, 7269 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 357, 7269?
Answer: HCF of 357, 7269 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 7269 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 7269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.