Highest Common Factor of 745, 2322 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 745, 2322 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 745, 2322 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 745, 2322 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 745, 2322 is 1.
HCF(745, 2322) = 1
HCF of 745, 2322 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 745, 2322 is 1.
Highest Common Factor of 745,2322 is 1
Step 1: Since 2322 > 745, we apply the division lemma to 2322 and 745, to get
2322 = 745 x 3 + 87
Step 2: Since the reminder 745 ≠ 0, we apply division lemma to 87 and 745, to get
745 = 87 x 8 + 49
Step 3: We consider the new divisor 87 and the new remainder 49, and apply the division lemma to get
87 = 49 x 1 + 38
We consider the new divisor 49 and the new remainder 38,and apply the division lemma to get
49 = 38 x 1 + 11
We consider the new divisor 38 and the new remainder 11,and apply the division lemma to get
38 = 11 x 3 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 745 and 2322 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(38,11) = HCF(49,38) = HCF(87,49) = HCF(745,87) = HCF(2322,745) .
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Frequently Asked Questions on HCF of 745, 2322 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 745, 2322?
Answer: HCF of 745, 2322 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 745, 2322 using Euclid's Algorithm?
Answer: For arbitrary numbers 745, 2322 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.