Highest Common Factor of 735, 528 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, 528 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 528 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 735, 528 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, 528 is 3.
HCF(735, 528) = 3
HCF of 735, 528 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, 528 is 3.
Highest Common Factor of 735,528 is 3
Step 1: Since 735 > 528, we apply the division lemma to 735 and 528, to get
735 = 528 x 1 + 207
Step 2: Since the reminder 528 ≠ 0, we apply division lemma to 207 and 528, to get
528 = 207 x 2 + 114
Step 3: We consider the new divisor 207 and the new remainder 114, and apply the division lemma to get
207 = 114 x 1 + 93
We consider the new divisor 114 and the new remainder 93,and apply the division lemma to get
114 = 93 x 1 + 21
We consider the new divisor 93 and the new remainder 21,and apply the division lemma to get
93 = 21 x 4 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 735 and 528 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(93,21) = HCF(114,93) = HCF(207,114) = HCF(528,207) = HCF(735,528) .
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Frequently Asked Questions on HCF of 735, 528 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, 528?
Answer: HCF of 735, 528 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 528 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 528 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.