Highest Common Factor of 900, 345, 68 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 900, 345, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 900, 345, 68 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 900, 345, 68 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 900, 345, 68 is 1.
HCF(900, 345, 68) = 1
HCF of 900, 345, 68 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 900, 345, 68 is 1.
Highest Common Factor of 900,345,68 is 1
Step 1: Since 900 > 345, we apply the division lemma to 900 and 345, to get
900 = 345 x 2 + 210
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 210 and 345, to get
345 = 210 x 1 + 135
Step 3: We consider the new divisor 210 and the new remainder 135, and apply the division lemma to get
210 = 135 x 1 + 75
We consider the new divisor 135 and the new remainder 75,and apply the division lemma to get
135 = 75 x 1 + 60
We consider the new divisor 75 and the new remainder 60,and apply the division lemma to get
75 = 60 x 1 + 15
We consider the new divisor 60 and the new remainder 15,and apply the division lemma to get
60 = 15 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 900 and 345 is 15
Notice that 15 = HCF(60,15) = HCF(75,60) = HCF(135,75) = HCF(210,135) = HCF(345,210) = HCF(900,345) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 15, we apply the division lemma to 68 and 15, to get
68 = 15 x 4 + 8
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 8 and 15, to get
15 = 8 x 1 + 7
Step 3: We consider the new divisor 8 and the new remainder 7, and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1, and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 68 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(15,8) = HCF(68,15) .
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Frequently Asked Questions on HCF of 900, 345, 68 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 900, 345, 68?
Answer: HCF of 900, 345, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 900, 345, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 900, 345, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.