Highest Common Factor of 454, 13936 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 454, 13936 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 454, 13936 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 454, 13936 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 454, 13936 is 2.
HCF(454, 13936) = 2
HCF of 454, 13936 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 454, 13936 is 2.
Highest Common Factor of 454,13936 is 2
Step 1: Since 13936 > 454, we apply the division lemma to 13936 and 454, to get
13936 = 454 x 30 + 316
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 316 and 454, to get
454 = 316 x 1 + 138
Step 3: We consider the new divisor 316 and the new remainder 138, and apply the division lemma to get
316 = 138 x 2 + 40
We consider the new divisor 138 and the new remainder 40,and apply the division lemma to get
138 = 40 x 3 + 18
We consider the new divisor 40 and the new remainder 18,and apply the division lemma to get
40 = 18 x 2 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 454 and 13936 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(40,18) = HCF(138,40) = HCF(316,138) = HCF(454,316) = HCF(13936,454) .
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Frequently Asked Questions on HCF of 454, 13936 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 454, 13936?
Answer: HCF of 454, 13936 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 454, 13936 using Euclid's Algorithm?
Answer: For arbitrary numbers 454, 13936 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.