Highest Common Factor of 374, 3222, 5739 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 374, 3222, 5739 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 374, 3222, 5739 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 374, 3222, 5739 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 374, 3222, 5739 is 1.
HCF(374, 3222, 5739) = 1
HCF of 374, 3222, 5739 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 374, 3222, 5739 is 1.
Highest Common Factor of 374,3222,5739 is 1
Step 1: Since 3222 > 374, we apply the division lemma to 3222 and 374, to get
3222 = 374 x 8 + 230
Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 230 and 374, to get
374 = 230 x 1 + 144
Step 3: We consider the new divisor 230 and the new remainder 144, and apply the division lemma to get
230 = 144 x 1 + 86
We consider the new divisor 144 and the new remainder 86,and apply the division lemma to get
144 = 86 x 1 + 58
We consider the new divisor 86 and the new remainder 58,and apply the division lemma to get
86 = 58 x 1 + 28
We consider the new divisor 58 and the new remainder 28,and apply the division lemma to get
58 = 28 x 2 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 374 and 3222 is 2
Notice that 2 = HCF(28,2) = HCF(58,28) = HCF(86,58) = HCF(144,86) = HCF(230,144) = HCF(374,230) = HCF(3222,374) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5739 > 2, we apply the division lemma to 5739 and 2, to get
5739 = 2 x 2869 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 5739 is 1
Notice that 1 = HCF(2,1) = HCF(5739,2) .
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Frequently Asked Questions on HCF of 374, 3222, 5739 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 374, 3222, 5739?
Answer: HCF of 374, 3222, 5739 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 374, 3222, 5739 using Euclid's Algorithm?
Answer: For arbitrary numbers 374, 3222, 5739 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.