Highest Common Factor of 6419, 840 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 6419, 840 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 6419, 840 is 7 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 6419, 840 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 6419, 840 is 7.
HCF(6419, 840) = 7
HCF of 6419, 840 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6419, 840 is 7.
Highest Common Factor of 6419,840 is 7
Step 1: Since 6419 > 840, we apply the division lemma to 6419 and 840, to get
6419 = 840 x 7 + 539
Step 2: Since the reminder 840 ≠ 0, we apply division lemma to 539 and 840, to get
840 = 539 x 1 + 301
Step 3: We consider the new divisor 539 and the new remainder 301, and apply the division lemma to get
539 = 301 x 1 + 238
We consider the new divisor 301 and the new remainder 238,and apply the division lemma to get
301 = 238 x 1 + 63
We consider the new divisor 238 and the new remainder 63,and apply the division lemma to get
238 = 63 x 3 + 49
We consider the new divisor 63 and the new remainder 49,and apply the division lemma to get
63 = 49 x 1 + 14
We consider the new divisor 49 and the new remainder 14,and apply the division lemma to get
49 = 14 x 3 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 6419 and 840 is 7
Notice that 7 = HCF(14,7) = HCF(49,14) = HCF(63,49) = HCF(238,63) = HCF(301,238) = HCF(539,301) = HCF(840,539) = HCF(6419,840) .
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Frequently Asked Questions on HCF of 6419, 840 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 6419, 840?
Answer: HCF of 6419, 840 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6419, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 6419, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.