Highest Common Factor of 1945, 3738 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 1945, 3738 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1945, 3738 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 1945, 3738 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 1945, 3738 is 1.
HCF(1945, 3738) = 1
HCF of 1945, 3738 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1945, 3738 is 1.
Highest Common Factor of 1945,3738 is 1
Step 1: Since 3738 > 1945, we apply the division lemma to 3738 and 1945, to get
3738 = 1945 x 1 + 1793
Step 2: Since the reminder 1945 ≠ 0, we apply division lemma to 1793 and 1945, to get
1945 = 1793 x 1 + 152
Step 3: We consider the new divisor 1793 and the new remainder 152, and apply the division lemma to get
1793 = 152 x 11 + 121
We consider the new divisor 152 and the new remainder 121,and apply the division lemma to get
152 = 121 x 1 + 31
We consider the new divisor 121 and the new remainder 31,and apply the division lemma to get
121 = 31 x 3 + 28
We consider the new divisor 31 and the new remainder 28,and apply the division lemma to get
31 = 28 x 1 + 3
We consider the new divisor 28 and the new remainder 3,and apply the division lemma to get
28 = 3 x 9 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1945 and 3738 is 1
Notice that 1 = HCF(3,1) = HCF(28,3) = HCF(31,28) = HCF(121,31) = HCF(152,121) = HCF(1793,152) = HCF(1945,1793) = HCF(3738,1945) .
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Frequently Asked Questions on HCF of 1945, 3738 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 1945, 3738?
Answer: HCF of 1945, 3738 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1945, 3738 using Euclid's Algorithm?
Answer: For arbitrary numbers 1945, 3738 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.