Highest Common Factor of 3423, 4984, 31572 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 3423, 4984, 31572 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3423, 4984, 31572 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 3423, 4984, 31572 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 3423, 4984, 31572 is 1.
HCF(3423, 4984, 31572) = 1
HCF of 3423, 4984, 31572 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3423, 4984, 31572 is 1.
Highest Common Factor of 3423,4984,31572 is 1
Step 1: Since 4984 > 3423, we apply the division lemma to 4984 and 3423, to get
4984 = 3423 x 1 + 1561
Step 2: Since the reminder 3423 ≠ 0, we apply division lemma to 1561 and 3423, to get
3423 = 1561 x 2 + 301
Step 3: We consider the new divisor 1561 and the new remainder 301, and apply the division lemma to get
1561 = 301 x 5 + 56
We consider the new divisor 301 and the new remainder 56,and apply the division lemma to get
301 = 56 x 5 + 21
We consider the new divisor 56 and the new remainder 21,and apply the division lemma to get
56 = 21 x 2 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 3423 and 4984 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(56,21) = HCF(301,56) = HCF(1561,301) = HCF(3423,1561) = HCF(4984,3423) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31572 > 7, we apply the division lemma to 31572 and 7, to get
31572 = 7 x 4510 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 31572 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(31572,7) .
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Frequently Asked Questions on HCF of 3423, 4984, 31572 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 3423, 4984, 31572?
Answer: HCF of 3423, 4984, 31572 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3423, 4984, 31572 using Euclid's Algorithm?
Answer: For arbitrary numbers 3423, 4984, 31572 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
