Highest Common Factor of 749, 2138 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 749, 2138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 749, 2138 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 749, 2138 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 749, 2138 is 1.
HCF(749, 2138) = 1
HCF of 749, 2138 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 749, 2138 is 1.
Highest Common Factor of 749,2138 is 1
Step 1: Since 2138 > 749, we apply the division lemma to 2138 and 749, to get
2138 = 749 x 2 + 640
Step 2: Since the reminder 749 ≠ 0, we apply division lemma to 640 and 749, to get
749 = 640 x 1 + 109
Step 3: We consider the new divisor 640 and the new remainder 109, and apply the division lemma to get
640 = 109 x 5 + 95
We consider the new divisor 109 and the new remainder 95,and apply the division lemma to get
109 = 95 x 1 + 14
We consider the new divisor 95 and the new remainder 14,and apply the division lemma to get
95 = 14 x 6 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 749 and 2138 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(95,14) = HCF(109,95) = HCF(640,109) = HCF(749,640) = HCF(2138,749) .
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Frequently Asked Questions on HCF of 749, 2138 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 749, 2138?
Answer: HCF of 749, 2138 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 749, 2138 using Euclid's Algorithm?
Answer: For arbitrary numbers 749, 2138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
