Highest Common Factor of 735, 665, 402 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, 665, 402 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 665, 402 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, 665, 402 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, 665, 402 is 1.
HCF(735, 665, 402) = 1
HCF of 735, 665, 402 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, 665, 402 is 1.
Highest Common Factor of 735,665,402 is 1
Step 1: Since 735 > 665, we apply the division lemma to 735 and 665, to get
735 = 665 x 1 + 70
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 70 and 665, to get
665 = 70 x 9 + 35
Step 3: We consider the new divisor 70 and the new remainder 35, and apply the division lemma to get
70 = 35 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 735 and 665 is 35
Notice that 35 = HCF(70,35) = HCF(665,70) = HCF(735,665) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 402 > 35, we apply the division lemma to 402 and 35, to get
402 = 35 x 11 + 17
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 17 and 35, to get
35 = 17 x 2 + 1
Step 3: We consider the new divisor 17 and the new remainder 1, and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 35 and 402 is 1
Notice that 1 = HCF(17,1) = HCF(35,17) = HCF(402,35) .
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Frequently Asked Questions on HCF of 735, 665, 402 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, 665, 402?
Answer: HCF of 735, 665, 402 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 665, 402 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 665, 402 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.