Highest Common Factor of 872, 3754 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 872, 3754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 872, 3754 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 872, 3754 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 872, 3754 is 2.
HCF(872, 3754) = 2
HCF of 872, 3754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 872, 3754 is 2.
Highest Common Factor of 872,3754 is 2
Step 1: Since 3754 > 872, we apply the division lemma to 3754 and 872, to get
3754 = 872 x 4 + 266
Step 2: Since the reminder 872 ≠ 0, we apply division lemma to 266 and 872, to get
872 = 266 x 3 + 74
Step 3: We consider the new divisor 266 and the new remainder 74, and apply the division lemma to get
266 = 74 x 3 + 44
We consider the new divisor 74 and the new remainder 44,and apply the division lemma to get
74 = 44 x 1 + 30
We consider the new divisor 44 and the new remainder 30,and apply the division lemma to get
44 = 30 x 1 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 872 and 3754 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(44,30) = HCF(74,44) = HCF(266,74) = HCF(872,266) = HCF(3754,872) .
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Frequently Asked Questions on HCF of 872, 3754 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 872, 3754?
Answer: HCF of 872, 3754 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 872, 3754 using Euclid's Algorithm?
Answer: For arbitrary numbers 872, 3754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.