Highest Common Factor of 966, 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 966, 735 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 966, 735 is 21 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 966, 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 966, 735 is 21.
HCF(966, 735) = 21
HCF of 966, 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 966, 735 is 21.
Highest Common Factor of 966,735 is 21
Step 1: Since 966 > 735, we apply the division lemma to 966 and 735, to get
966 = 735 x 1 + 231
Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 231 and 735, to get
735 = 231 x 3 + 42
Step 3: We consider the new divisor 231 and the new remainder 42, and apply the division lemma to get
231 = 42 x 5 + 21
We consider the new divisor 42 and the new remainder 21, and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 966 and 735 is 21
Notice that 21 = HCF(42,21) = HCF(231,42) = HCF(735,231) = HCF(966,735) .
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Frequently Asked Questions on HCF of 966, 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 966, 735?
Answer: HCF of 966, 735 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 966, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 966, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.