Highest Common Factor of 872, 14508 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, 14508 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 872, 14508 is 4 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, 14508 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, 14508 is 4.
HCF(872, 14508) = 4
HCF of 872, 14508 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, 14508 is 4.
Highest Common Factor of 872,14508 is 4
Step 1: Since 14508 > 872, we apply the division lemma to 14508 and 872, to get
14508 = 872 x 16 + 556
Step 2: Since the reminder 872 ≠ 0, we apply division lemma to 556 and 872, to get
872 = 556 x 1 + 316
Step 3: We consider the new divisor 556 and the new remainder 316, and apply the division lemma to get
556 = 316 x 1 + 240
We consider the new divisor 316 and the new remainder 240,and apply the division lemma to get
316 = 240 x 1 + 76
We consider the new divisor 240 and the new remainder 76,and apply the division lemma to get
240 = 76 x 3 + 12
We consider the new divisor 76 and the new remainder 12,and apply the division lemma to get
76 = 12 x 6 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 872 and 14508 is 4
Notice that 4 = HCF(12,4) = HCF(76,12) = HCF(240,76) = HCF(316,240) = HCF(556,316) = HCF(872,556) = HCF(14508,872) .
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Frequently Asked Questions on HCF of 872, 14508 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, 14508?
Answer: HCF of 872, 14508 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 872, 14508 using Euclid's Algorithm?
Answer: For arbitrary numbers 872, 14508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.