Highest Common Factor of 1410, 6914 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 1410, 6914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1410, 6914 is 2 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 1410, 6914 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 1410, 6914 is 2.
HCF(1410, 6914) = 2
HCF of 1410, 6914 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1410, 6914 is 2.
Highest Common Factor of 1410,6914 is 2
Step 1: Since 6914 > 1410, we apply the division lemma to 6914 and 1410, to get
6914 = 1410 x 4 + 1274
Step 2: Since the reminder 1410 ≠ 0, we apply division lemma to 1274 and 1410, to get
1410 = 1274 x 1 + 136
Step 3: We consider the new divisor 1274 and the new remainder 136, and apply the division lemma to get
1274 = 136 x 9 + 50
We consider the new divisor 136 and the new remainder 50,and apply the division lemma to get
136 = 50 x 2 + 36
We consider the new divisor 50 and the new remainder 36,and apply the division lemma to get
50 = 36 x 1 + 14
We consider the new divisor 36 and the new remainder 14,and apply the division lemma to get
36 = 14 x 2 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1410 and 6914 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(36,14) = HCF(50,36) = HCF(136,50) = HCF(1274,136) = HCF(1410,1274) = HCF(6914,1410) .
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Frequently Asked Questions on HCF of 1410, 6914 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 1410, 6914?
Answer: HCF of 1410, 6914 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1410, 6914 using Euclid's Algorithm?
Answer: For arbitrary numbers 1410, 6914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.