Highest Common Factor of 708, 300, 78 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 708, 300, 78 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 300, 78 is 6 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 708, 300, 78 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 708, 300, 78 is 6.
HCF(708, 300, 78) = 6
HCF of 708, 300, 78 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 708, 300, 78 is 6.
Highest Common Factor of 708,300,78 is 6
Step 1: Since 708 > 300, we apply the division lemma to 708 and 300, to get
708 = 300 x 2 + 108
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 108 and 300, to get
300 = 108 x 2 + 84
Step 3: We consider the new divisor 108 and the new remainder 84, and apply the division lemma to get
108 = 84 x 1 + 24
We consider the new divisor 84 and the new remainder 24,and apply the division lemma to get
84 = 24 x 3 + 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 708 and 300 is 12
Notice that 12 = HCF(24,12) = HCF(84,24) = HCF(108,84) = HCF(300,108) = HCF(708,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 12, we apply the division lemma to 78 and 12, to get
78 = 12 x 6 + 6
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, 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 12 and 78 is 6
Notice that 6 = HCF(12,6) = HCF(78,12) .
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Frequently Asked Questions on HCF of 708, 300, 78 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 708, 300, 78?
Answer: HCF of 708, 300, 78 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 300, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 300, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.