Highest Common Factor of 702, 1728, 8448 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 702, 1728, 8448 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 702, 1728, 8448 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 702, 1728, 8448 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 702, 1728, 8448 is 6.
HCF(702, 1728, 8448) = 6
HCF of 702, 1728, 8448 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 702, 1728, 8448 is 6.
Highest Common Factor of 702,1728,8448 is 6
Step 1: Since 1728 > 702, we apply the division lemma to 1728 and 702, to get
1728 = 702 x 2 + 324
Step 2: Since the reminder 702 ≠ 0, we apply division lemma to 324 and 702, to get
702 = 324 x 2 + 54
Step 3: We consider the new divisor 324 and the new remainder 54, and apply the division lemma to get
324 = 54 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 702 and 1728 is 54
Notice that 54 = HCF(324,54) = HCF(702,324) = HCF(1728,702) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8448 > 54, we apply the division lemma to 8448 and 54, to get
8448 = 54 x 156 + 24
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 24 and 54, to get
54 = 24 x 2 + 6
Step 3: We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 54 and 8448 is 6
Notice that 6 = HCF(24,6) = HCF(54,24) = HCF(8448,54) .
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Frequently Asked Questions on HCF of 702, 1728, 8448 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 702, 1728, 8448?
Answer: HCF of 702, 1728, 8448 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 702, 1728, 8448 using Euclid's Algorithm?
Answer: For arbitrary numbers 702, 1728, 8448 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.