Highest Common Factor of 345, 5992, 9953 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 345, 5992, 9953 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 5992, 9953 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 345, 5992, 9953 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 345, 5992, 9953 is 1.
HCF(345, 5992, 9953) = 1
HCF of 345, 5992, 9953 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 345, 5992, 9953 is 1.
Highest Common Factor of 345,5992,9953 is 1
Step 1: Since 5992 > 345, we apply the division lemma to 5992 and 345, to get
5992 = 345 x 17 + 127
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 127 and 345, to get
345 = 127 x 2 + 91
Step 3: We consider the new divisor 127 and the new remainder 91, and apply the division lemma to get
127 = 91 x 1 + 36
We consider the new divisor 91 and the new remainder 36,and apply the division lemma to get
91 = 36 x 2 + 19
We consider the new divisor 36 and the new remainder 19,and apply the division lemma to get
36 = 19 x 1 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 345 and 5992 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(36,19) = HCF(91,36) = HCF(127,91) = HCF(345,127) = HCF(5992,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9953 > 1, we apply the division lemma to 9953 and 1, to get
9953 = 1 x 9953 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9953 is 1
Notice that 1 = HCF(9953,1) .
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Frequently Asked Questions on HCF of 345, 5992, 9953 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 345, 5992, 9953?
Answer: HCF of 345, 5992, 9953 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 5992, 9953 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 5992, 9953 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.