Highest Common Factor of 715, 975, 640 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 715, 975, 640 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 715, 975, 640 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 715, 975, 640 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 715, 975, 640 is 5.
HCF(715, 975, 640) = 5
HCF of 715, 975, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 715, 975, 640 is 5.
Highest Common Factor of 715,975,640 is 5
Step 1: Since 975 > 715, we apply the division lemma to 975 and 715, to get
975 = 715 x 1 + 260
Step 2: Since the reminder 715 ≠ 0, we apply division lemma to 260 and 715, to get
715 = 260 x 2 + 195
Step 3: We consider the new divisor 260 and the new remainder 195, and apply the division lemma to get
260 = 195 x 1 + 65
We consider the new divisor 195 and the new remainder 65, and apply the division lemma to get
195 = 65 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 65, the HCF of 715 and 975 is 65
Notice that 65 = HCF(195,65) = HCF(260,195) = HCF(715,260) = HCF(975,715) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 640 > 65, we apply the division lemma to 640 and 65, to get
640 = 65 x 9 + 55
Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 55 and 65, to get
65 = 55 x 1 + 10
Step 3: We consider the new divisor 55 and the new remainder 10, and apply the division lemma to get
55 = 10 x 5 + 5
We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 65 and 640 is 5
Notice that 5 = HCF(10,5) = HCF(55,10) = HCF(65,55) = HCF(640,65) .
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Frequently Asked Questions on HCF of 715, 975, 640 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 715, 975, 640?
Answer: HCF of 715, 975, 640 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 715, 975, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 715, 975, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
