Highest Common Factor of 340, 714, 975 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, 714, 975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 714, 975 is 1 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, 714, 975 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, 714, 975 is 1.
HCF(340, 714, 975) = 1
HCF of 340, 714, 975 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, 714, 975 is 1.
Highest Common Factor of 340,714,975 is 1
Step 1: Since 714 > 340, we apply the division lemma to 714 and 340, to get
714 = 340 x 2 + 34
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 34 and 340, to get
340 = 34 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 340 and 714 is 34
Notice that 34 = HCF(340,34) = HCF(714,340) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 975 > 34, we apply the division lemma to 975 and 34, to get
975 = 34 x 28 + 23
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 23 and 34, to get
34 = 23 x 1 + 11
Step 3: We consider the new divisor 23 and the new remainder 11, and apply the division lemma to get
23 = 11 x 2 + 1
We consider the new divisor 11 and the new remainder 1, and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 34 and 975 is 1
Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(34,23) = HCF(975,34) .
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Frequently Asked Questions on HCF of 340, 714, 975 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, 714, 975?
Answer: HCF of 340, 714, 975 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 714, 975 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 714, 975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.