Highest Common Factor of 708, 453, 18 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, 453, 18 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 708, 453, 18 is 3 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, 453, 18 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, 453, 18 is 3.
HCF(708, 453, 18) = 3
HCF of 708, 453, 18 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, 453, 18 is 3.
Highest Common Factor of 708,453,18 is 3
Step 1: Since 708 > 453, we apply the division lemma to 708 and 453, to get
708 = 453 x 1 + 255
Step 2: Since the reminder 453 ≠ 0, we apply division lemma to 255 and 453, to get
453 = 255 x 1 + 198
Step 3: We consider the new divisor 255 and the new remainder 198, and apply the division lemma to get
255 = 198 x 1 + 57
We consider the new divisor 198 and the new remainder 57,and apply the division lemma to get
198 = 57 x 3 + 27
We consider the new divisor 57 and the new remainder 27,and apply the division lemma to get
57 = 27 x 2 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 708 and 453 is 3
Notice that 3 = HCF(27,3) = HCF(57,27) = HCF(198,57) = HCF(255,198) = HCF(453,255) = HCF(708,453) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18 > 3, we apply the division lemma to 18 and 3, to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 18 is 3
Notice that 3 = HCF(18,3) .
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Frequently Asked Questions on HCF of 708, 453, 18 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, 453, 18?
Answer: HCF of 708, 453, 18 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 708, 453, 18 using Euclid's Algorithm?
Answer: For arbitrary numbers 708, 453, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.