Highest Common Factor of 402, 2188, 3572 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, 2188, 3572 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 402, 2188, 3572 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, 2188, 3572 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, 2188, 3572 is 2.
HCF(402, 2188, 3572) = 2
HCF of 402, 2188, 3572 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, 2188, 3572 is 2.
Highest Common Factor of 402,2188,3572 is 2
Step 1: Since 2188 > 402, we apply the division lemma to 2188 and 402, to get
2188 = 402 x 5 + 178
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 178 and 402, to get
402 = 178 x 2 + 46
Step 3: We consider the new divisor 178 and the new remainder 46, and apply the division lemma to get
178 = 46 x 3 + 40
We consider the new divisor 46 and the new remainder 40,and apply the division lemma to get
46 = 40 x 1 + 6
We consider the new divisor 40 and the new remainder 6,and apply the division lemma to get
40 = 6 x 6 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
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 402 and 2188 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(46,40) = HCF(178,46) = HCF(402,178) = HCF(2188,402) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3572 > 2, we apply the division lemma to 3572 and 2, to get
3572 = 2 x 1786 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 3572 is 2
Notice that 2 = HCF(3572,2) .
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Frequently Asked Questions on HCF of 402, 2188, 3572 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, 2188, 3572?
Answer: HCF of 402, 2188, 3572 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 402, 2188, 3572 using Euclid's Algorithm?
Answer: For arbitrary numbers 402, 2188, 3572 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.