Highest Common Factor of 1407, 1842 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 1407, 1842 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1407, 1842 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 1407, 1842 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 1407, 1842 is 3.
HCF(1407, 1842) = 3
HCF of 1407, 1842 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1407, 1842 is 3.
Highest Common Factor of 1407,1842 is 3
Step 1: Since 1842 > 1407, we apply the division lemma to 1842 and 1407, to get
1842 = 1407 x 1 + 435
Step 2: Since the reminder 1407 ≠ 0, we apply division lemma to 435 and 1407, to get
1407 = 435 x 3 + 102
Step 3: We consider the new divisor 435 and the new remainder 102, and apply the division lemma to get
435 = 102 x 4 + 27
We consider the new divisor 102 and the new remainder 27,and apply the division lemma to get
102 = 27 x 3 + 21
We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get
27 = 21 x 1 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1407 and 1842 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(102,27) = HCF(435,102) = HCF(1407,435) = HCF(1842,1407) .
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Frequently Asked Questions on HCF of 1407, 1842 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 1407, 1842?
Answer: HCF of 1407, 1842 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1407, 1842 using Euclid's Algorithm?
Answer: For arbitrary numbers 1407, 1842 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.