Highest Common Factor of 342, 906, 65 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 342, 906, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 342, 906, 65 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 342, 906, 65 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 342, 906, 65 is 1.
HCF(342, 906, 65) = 1
HCF of 342, 906, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 342, 906, 65 is 1.
Highest Common Factor of 342,906,65 is 1
Step 1: Since 906 > 342, we apply the division lemma to 906 and 342, to get
906 = 342 x 2 + 222
Step 2: Since the reminder 342 ≠ 0, we apply division lemma to 222 and 342, to get
342 = 222 x 1 + 120
Step 3: We consider the new divisor 222 and the new remainder 120, and apply the division lemma to get
222 = 120 x 1 + 102
We consider the new divisor 120 and the new remainder 102,and apply the division lemma to get
120 = 102 x 1 + 18
We consider the new divisor 102 and the new remainder 18,and apply the division lemma to get
102 = 18 x 5 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 342 and 906 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(102,18) = HCF(120,102) = HCF(222,120) = HCF(342,222) = HCF(906,342) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 6, we apply the division lemma to 65 and 6, to get
65 = 6 x 10 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: 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 6 and 65 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(65,6) .
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Frequently Asked Questions on HCF of 342, 906, 65 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 342, 906, 65?
Answer: HCF of 342, 906, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 342, 906, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 342, 906, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.