Highest Common Factor of 664, 498, 735 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 664, 498, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 664, 498, 735 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 664, 498, 735 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 664, 498, 735 is 1.
HCF(664, 498, 735) = 1
HCF of 664, 498, 735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 664, 498, 735 is 1.
Highest Common Factor of 664,498,735 is 1
Step 1: Since 664 > 498, we apply the division lemma to 664 and 498, to get
664 = 498 x 1 + 166
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 166 and 498, to get
498 = 166 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 166, the HCF of 664 and 498 is 166
Notice that 166 = HCF(498,166) = HCF(664,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 166, we apply the division lemma to 735 and 166, to get
735 = 166 x 4 + 71
Step 2: Since the reminder 166 ≠ 0, we apply division lemma to 71 and 166, to get
166 = 71 x 2 + 24
Step 3: We consider the new divisor 71 and the new remainder 24, and apply the division lemma to get
71 = 24 x 2 + 23
We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get
24 = 23 x 1 + 1
We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get
23 = 1 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 166 and 735 is 1
Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(71,24) = HCF(166,71) = HCF(735,166) .
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Frequently Asked Questions on HCF of 664, 498, 735 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 664, 498, 735?
Answer: HCF of 664, 498, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 664, 498, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 664, 498, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.