Highest Common Factor of 96, 60, 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 96, 60, 68 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 96, 60, 68 is 4 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 96, 60, 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 96, 60, 68 is 4.
HCF(96, 60, 68) = 4
HCF of 96, 60, 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 96, 60, 68 is 4.
Highest Common Factor of 96,60,68 is 4
Step 1: Since 96 > 60, we apply the division lemma to 96 and 60, to get
96 = 60 x 1 + 36
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 36 and 60, to get
60 = 36 x 1 + 24
Step 3: We consider the new divisor 36 and the new remainder 24, and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12, and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 96 and 60 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(60,36) = HCF(96,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 12, we apply the division lemma to 68 and 12, to get
68 = 12 x 5 + 8
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 8 and 12, to get
12 = 8 x 1 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 12 and 68 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(68,12) .
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Frequently Asked Questions on HCF of 96, 60, 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 96, 60, 68?
Answer: HCF of 96, 60, 68 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 96, 60, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 96, 60, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.