Highest Common Factor of 735, 940 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, 940 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 940 is 5 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, 940 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, 940 is 5.
HCF(735, 940) = 5
HCF of 735, 940 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, 940 is 5.
Highest Common Factor of 735,940 is 5
Step 1: Since 940 > 735, we apply the division lemma to 940 and 735, to get
940 = 735 x 1 + 205
Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 205 and 735, to get
735 = 205 x 3 + 120
Step 3: We consider the new divisor 205 and the new remainder 120, and apply the division lemma to get
205 = 120 x 1 + 85
We consider the new divisor 120 and the new remainder 85,and apply the division lemma to get
120 = 85 x 1 + 35
We consider the new divisor 85 and the new remainder 35,and apply the division lemma to get
85 = 35 x 2 + 15
We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get
35 = 15 x 2 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 735 and 940 is 5
Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(85,35) = HCF(120,85) = HCF(205,120) = HCF(735,205) = HCF(940,735) .
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Frequently Asked Questions on HCF of 735, 940 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, 940?
Answer: HCF of 735, 940 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 940 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 940 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.