Highest Common Factor of 741, 646, 508 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 741, 646, 508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 741, 646, 508 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 741, 646, 508 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 741, 646, 508 is 1.
HCF(741, 646, 508) = 1
HCF of 741, 646, 508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 741, 646, 508 is 1.
Highest Common Factor of 741,646,508 is 1
Step 1: Since 741 > 646, we apply the division lemma to 741 and 646, to get
741 = 646 x 1 + 95
Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 95 and 646, to get
646 = 95 x 6 + 76
Step 3: We consider the new divisor 95 and the new remainder 76, and apply the division lemma to get
95 = 76 x 1 + 19
We consider the new divisor 76 and the new remainder 19, and apply the division lemma to get
76 = 19 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 741 and 646 is 19
Notice that 19 = HCF(76,19) = HCF(95,76) = HCF(646,95) = HCF(741,646) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 508 > 19, we apply the division lemma to 508 and 19, to get
508 = 19 x 26 + 14
Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 14 and 19, to get
19 = 14 x 1 + 5
Step 3: We consider the new divisor 14 and the new remainder 5, and apply the division lemma to get
14 = 5 x 2 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 19 and 508 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(508,19) .
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Frequently Asked Questions on HCF of 741, 646, 508 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 741, 646, 508?
Answer: HCF of 741, 646, 508 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 741, 646, 508 using Euclid's Algorithm?
Answer: For arbitrary numbers 741, 646, 508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.