Highest Common Factor of 357, 849 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, 849 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 849 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, 849 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, 849 is 3.
HCF(357, 849) = 3
HCF of 357, 849 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, 849 is 3.
Highest Common Factor of 357,849 is 3
Step 1: Since 849 > 357, we apply the division lemma to 849 and 357, to get
849 = 357 x 2 + 135
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 135 and 357, to get
357 = 135 x 2 + 87
Step 3: We consider the new divisor 135 and the new remainder 87, and apply the division lemma to get
135 = 87 x 1 + 48
We consider the new divisor 87 and the new remainder 48,and apply the division lemma to get
87 = 48 x 1 + 39
We consider the new divisor 48 and the new remainder 39,and apply the division lemma to get
48 = 39 x 1 + 9
We consider the new divisor 39 and the new remainder 9,and apply the division lemma to get
39 = 9 x 4 + 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 849 is 3
Notice that 3 = HCF(9,3) = HCF(39,9) = HCF(48,39) = HCF(87,48) = HCF(135,87) = HCF(357,135) = HCF(849,357) .
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Frequently Asked Questions on HCF of 357, 849 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, 849?
Answer: HCF of 357, 849 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 849 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 849 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
