Highest Common Factor of 499, 138 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 499, 138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 499, 138 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 499, 138 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 499, 138 is 1.
HCF(499, 138) = 1
HCF of 499, 138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 499, 138 is 1.
Highest Common Factor of 499,138 is 1
Step 1: Since 499 > 138, we apply the division lemma to 499 and 138, to get
499 = 138 x 3 + 85
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 85 and 138, to get
138 = 85 x 1 + 53
Step 3: We consider the new divisor 85 and the new remainder 53, and apply the division lemma to get
85 = 53 x 1 + 32
We consider the new divisor 53 and the new remainder 32,and apply the division lemma to get
53 = 32 x 1 + 21
We consider the new divisor 32 and the new remainder 21,and apply the division lemma to get
32 = 21 x 1 + 11
We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get
21 = 11 x 1 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 499 and 138 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(32,21) = HCF(53,32) = HCF(85,53) = HCF(138,85) = HCF(499,138) .
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Frequently Asked Questions on HCF of 499, 138 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 499, 138?
Answer: HCF of 499, 138 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 499, 138 using Euclid's Algorithm?
Answer: For arbitrary numbers 499, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
