Highest Common Factor of 357, 920, 113 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, 920, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 920, 113 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 357, 920, 113 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, 920, 113 is 1.
HCF(357, 920, 113) = 1
HCF of 357, 920, 113 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, 920, 113 is 1.
Highest Common Factor of 357,920,113 is 1
Step 1: Since 920 > 357, we apply the division lemma to 920 and 357, to get
920 = 357 x 2 + 206
Step 2: Since the reminder 357 ≠ 0, we apply division lemma to 206 and 357, to get
357 = 206 x 1 + 151
Step 3: We consider the new divisor 206 and the new remainder 151, and apply the division lemma to get
206 = 151 x 1 + 55
We consider the new divisor 151 and the new remainder 55,and apply the division lemma to get
151 = 55 x 2 + 41
We consider the new divisor 55 and the new remainder 41,and apply the division lemma to get
55 = 41 x 1 + 14
We consider the new divisor 41 and the new remainder 14,and apply the division lemma to get
41 = 14 x 2 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 357 and 920 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(41,14) = HCF(55,41) = HCF(151,55) = HCF(206,151) = HCF(357,206) = HCF(920,357) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 113 > 1, we apply the division lemma to 113 and 1, to get
113 = 1 x 113 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 113 is 1
Notice that 1 = HCF(113,1) .
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Frequently Asked Questions on HCF of 357, 920, 113 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, 920, 113?
Answer: HCF of 357, 920, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 920, 113 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 920, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
