Highest Common Factor of 898, 2132 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 898, 2132 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 898, 2132 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 898, 2132 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 898, 2132 is 2.
HCF(898, 2132) = 2
HCF of 898, 2132 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 898, 2132 is 2.
Highest Common Factor of 898,2132 is 2
Step 1: Since 2132 > 898, we apply the division lemma to 2132 and 898, to get
2132 = 898 x 2 + 336
Step 2: Since the reminder 898 ≠ 0, we apply division lemma to 336 and 898, to get
898 = 336 x 2 + 226
Step 3: We consider the new divisor 336 and the new remainder 226, and apply the division lemma to get
336 = 226 x 1 + 110
We consider the new divisor 226 and the new remainder 110,and apply the division lemma to get
226 = 110 x 2 + 6
We consider the new divisor 110 and the new remainder 6,and apply the division lemma to get
110 = 6 x 18 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 898 and 2132 is 2
Notice that 2 = HCF(6,2) = HCF(110,6) = HCF(226,110) = HCF(336,226) = HCF(898,336) = HCF(2132,898) .
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Frequently Asked Questions on HCF of 898, 2132 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 898, 2132?
Answer: HCF of 898, 2132 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 898, 2132 using Euclid's Algorithm?
Answer: For arbitrary numbers 898, 2132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.