Highest Common Factor of 402, 216, 556 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 402, 216, 556 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 402, 216, 556 is 2 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 402, 216, 556 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 402, 216, 556 is 2.
HCF(402, 216, 556) = 2
HCF of 402, 216, 556 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 402, 216, 556 is 2.
Highest Common Factor of 402,216,556 is 2
Step 1: Since 402 > 216, we apply the division lemma to 402 and 216, to get
402 = 216 x 1 + 186
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 186 and 216, to get
216 = 186 x 1 + 30
Step 3: We consider the new divisor 186 and the new remainder 30, and apply the division lemma to get
186 = 30 x 6 + 6
We consider the new divisor 30 and the new remainder 6, and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 402 and 216 is 6
Notice that 6 = HCF(30,6) = HCF(186,30) = HCF(216,186) = HCF(402,216) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 556 > 6, we apply the division lemma to 556 and 6, to get
556 = 6 x 92 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 556 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(556,6) .
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Frequently Asked Questions on HCF of 402, 216, 556 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 402, 216, 556?
Answer: HCF of 402, 216, 556 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 402, 216, 556 using Euclid's Algorithm?
Answer: For arbitrary numbers 402, 216, 556 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.