Highest Common Factor of 408, 706, 953 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 408, 706, 953 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 706, 953 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 408, 706, 953 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 408, 706, 953 is 1.
HCF(408, 706, 953) = 1
HCF of 408, 706, 953 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 706, 953 is 1.
Highest Common Factor of 408,706,953 is 1
Step 1: Since 706 > 408, we apply the division lemma to 706 and 408, to get
706 = 408 x 1 + 298
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 298 and 408, to get
408 = 298 x 1 + 110
Step 3: We consider the new divisor 298 and the new remainder 110, and apply the division lemma to get
298 = 110 x 2 + 78
We consider the new divisor 110 and the new remainder 78,and apply the division lemma to get
110 = 78 x 1 + 32
We consider the new divisor 78 and the new remainder 32,and apply the division lemma to get
78 = 32 x 2 + 14
We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get
32 = 14 x 2 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 408 and 706 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(78,32) = HCF(110,78) = HCF(298,110) = HCF(408,298) = HCF(706,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 953 > 2, we apply the division lemma to 953 and 2, to get
953 = 2 x 476 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 953 is 1
Notice that 1 = HCF(2,1) = HCF(953,2) .
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Frequently Asked Questions on HCF of 408, 706, 953 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 408, 706, 953?
Answer: HCF of 408, 706, 953 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 706, 953 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 706, 953 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
