Highest Common Factor of 735, 498, 671, 459 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 735, 498, 671, 459 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 498, 671, 459 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 735, 498, 671, 459 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 735, 498, 671, 459 is 1.
HCF(735, 498, 671, 459) = 1
HCF of 735, 498, 671, 459 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 735, 498, 671, 459 is 1.
Highest Common Factor of 735,498,671,459 is 1
Step 1: Since 735 > 498, we apply the division lemma to 735 and 498, to get
735 = 498 x 1 + 237
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 237 and 498, to get
498 = 237 x 2 + 24
Step 3: We consider the new divisor 237 and the new remainder 24, and apply the division lemma to get
237 = 24 x 9 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 735 and 498 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(237,24) = HCF(498,237) = HCF(735,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 671 > 3, we apply the division lemma to 671 and 3, to get
671 = 3 x 223 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 671 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(671,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 459 > 1, we apply the division lemma to 459 and 1, to get
459 = 1 x 459 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 459 is 1
Notice that 1 = HCF(459,1) .
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Frequently Asked Questions on HCF of 735, 498, 671, 459 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 735, 498, 671, 459?
Answer: HCF of 735, 498, 671, 459 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 498, 671, 459 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 498, 671, 459 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.