Highest Common Factor of 432, 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 432, 735 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 432, 735 is 3 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 432, 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 432, 735 is 3.
HCF(432, 735) = 3
HCF of 432, 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 432, 735 is 3.
Highest Common Factor of 432,735 is 3
Step 1: Since 735 > 432, we apply the division lemma to 735 and 432, to get
735 = 432 x 1 + 303
Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 303 and 432, to get
432 = 303 x 1 + 129
Step 3: We consider the new divisor 303 and the new remainder 129, and apply the division lemma to get
303 = 129 x 2 + 45
We consider the new divisor 129 and the new remainder 45,and apply the division lemma to get
129 = 45 x 2 + 39
We consider the new divisor 45 and the new remainder 39,and apply the division lemma to get
45 = 39 x 1 + 6
We consider the new divisor 39 and the new remainder 6,and apply the division lemma to get
39 = 6 x 6 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 432 and 735 is 3
Notice that 3 = HCF(6,3) = HCF(39,6) = HCF(45,39) = HCF(129,45) = HCF(303,129) = HCF(432,303) = HCF(735,432) .
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Frequently Asked Questions on HCF of 432, 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 432, 735?
Answer: HCF of 432, 735 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 432, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 432, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.