Highest Common Factor of 216, 357, 400 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 216, 357, 400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 216, 357, 400 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 216, 357, 400 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 216, 357, 400 is 1.
HCF(216, 357, 400) = 1
HCF of 216, 357, 400 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 216, 357, 400 is 1.
Highest Common Factor of 216,357,400 is 1
Step 1: Since 357 > 216, we apply the division lemma to 357 and 216, to get
357 = 216 x 1 + 141
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 141 and 216, to get
216 = 141 x 1 + 75
Step 3: We consider the new divisor 141 and the new remainder 75, and apply the division lemma to get
141 = 75 x 1 + 66
We consider the new divisor 75 and the new remainder 66,and apply the division lemma to get
75 = 66 x 1 + 9
We consider the new divisor 66 and the new remainder 9,and apply the division lemma to get
66 = 9 x 7 + 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 216 and 357 is 3
Notice that 3 = HCF(9,3) = HCF(66,9) = HCF(75,66) = HCF(141,75) = HCF(216,141) = HCF(357,216) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 400 > 3, we apply the division lemma to 400 and 3, to get
400 = 3 x 133 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 400 is 1
Notice that 1 = HCF(3,1) = HCF(400,3) .
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Frequently Asked Questions on HCF of 216, 357, 400 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 216, 357, 400?
Answer: HCF of 216, 357, 400 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 216, 357, 400 using Euclid's Algorithm?
Answer: For arbitrary numbers 216, 357, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.