Highest Common Factor of 645, 989, 112, 53 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 645, 989, 112, 53 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 989, 112, 53 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 645, 989, 112, 53 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 645, 989, 112, 53 is 1.
HCF(645, 989, 112, 53) = 1
HCF of 645, 989, 112, 53 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 989, 112, 53 is 1.
Highest Common Factor of 645,989,112,53 is 1
Step 1: Since 989 > 645, we apply the division lemma to 989 and 645, to get
989 = 645 x 1 + 344
Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 344 and 645, to get
645 = 344 x 1 + 301
Step 3: We consider the new divisor 344 and the new remainder 301, and apply the division lemma to get
344 = 301 x 1 + 43
We consider the new divisor 301 and the new remainder 43, and apply the division lemma to get
301 = 43 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 645 and 989 is 43
Notice that 43 = HCF(301,43) = HCF(344,301) = HCF(645,344) = HCF(989,645) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 112 > 43, we apply the division lemma to 112 and 43, to get
112 = 43 x 2 + 26
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 26 and 43, to get
43 = 26 x 1 + 17
Step 3: We consider the new divisor 26 and the new remainder 17, and apply the division lemma to get
26 = 17 x 1 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 112 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(26,17) = HCF(43,26) = HCF(112,43) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 53 > 1, we apply the division lemma to 53 and 1, to get
53 = 1 x 53 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 53 is 1
Notice that 1 = HCF(53,1) .
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Frequently Asked Questions on HCF of 645, 989, 112, 53 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 645, 989, 112, 53?
Answer: HCF of 645, 989, 112, 53 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 989, 112, 53 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 989, 112, 53 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.