Highest Common Factor of 340, 945 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 340, 945 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 945 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 340, 945 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 340, 945 is 5.
HCF(340, 945) = 5
HCF of 340, 945 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 945 is 5.
Highest Common Factor of 340,945 is 5
Step 1: Since 945 > 340, we apply the division lemma to 945 and 340, to get
945 = 340 x 2 + 265
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 265 and 340, to get
340 = 265 x 1 + 75
Step 3: We consider the new divisor 265 and the new remainder 75, and apply the division lemma to get
265 = 75 x 3 + 40
We consider the new divisor 75 and the new remainder 40,and apply the division lemma to get
75 = 40 x 1 + 35
We consider the new divisor 40 and the new remainder 35,and apply the division lemma to get
40 = 35 x 1 + 5
We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 340 and 945 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(75,40) = HCF(265,75) = HCF(340,265) = HCF(945,340) .
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Frequently Asked Questions on HCF of 340, 945 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 340, 945?
Answer: HCF of 340, 945 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 945 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 945 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.