Highest Common Factor of 345, 835, 972 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, 835, 972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 345, 835, 972 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, 835, 972 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, 835, 972 is 1.
HCF(345, 835, 972) = 1
HCF of 345, 835, 972 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, 835, 972 is 1.
Highest Common Factor of 345,835,972 is 1
Step 1: Since 835 > 345, we apply the division lemma to 835 and 345, to get
835 = 345 x 2 + 145
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 145 and 345, to get
345 = 145 x 2 + 55
Step 3: We consider the new divisor 145 and the new remainder 55, and apply the division lemma to get
145 = 55 x 2 + 35
We consider the new divisor 55 and the new remainder 35,and apply the division lemma to get
55 = 35 x 1 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 345 and 835 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(55,35) = HCF(145,55) = HCF(345,145) = HCF(835,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 972 > 5, we apply the division lemma to 972 and 5, to get
972 = 5 x 194 + 2
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get
5 = 2 x 2 + 1
Step 3: 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 5 and 972 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(972,5) .
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Frequently Asked Questions on HCF of 345, 835, 972 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, 835, 972?
Answer: HCF of 345, 835, 972 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 345, 835, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 345, 835, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
