Highest Common Factor of 408, 702, 787 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, 702, 787 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 702, 787 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, 702, 787 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, 702, 787 is 1.
HCF(408, 702, 787) = 1
HCF of 408, 702, 787 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, 702, 787 is 1.
Highest Common Factor of 408,702,787 is 1
Step 1: Since 702 > 408, we apply the division lemma to 702 and 408, to get
702 = 408 x 1 + 294
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 294 and 408, to get
408 = 294 x 1 + 114
Step 3: We consider the new divisor 294 and the new remainder 114, and apply the division lemma to get
294 = 114 x 2 + 66
We consider the new divisor 114 and the new remainder 66,and apply the division lemma to get
114 = 66 x 1 + 48
We consider the new divisor 66 and the new remainder 48,and apply the division lemma to get
66 = 48 x 1 + 18
We consider the new divisor 48 and the new remainder 18,and apply the division lemma to get
48 = 18 x 2 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma 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 408 and 702 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(48,18) = HCF(66,48) = HCF(114,66) = HCF(294,114) = HCF(408,294) = HCF(702,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 787 > 6, we apply the division lemma to 787 and 6, to get
787 = 6 x 131 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 787 is 1
Notice that 1 = HCF(6,1) = HCF(787,6) .
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Frequently Asked Questions on HCF of 408, 702, 787 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, 702, 787?
Answer: HCF of 408, 702, 787 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 702, 787 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 702, 787 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.