Highest Common Factor of 665, 1008 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 665, 1008 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 1008 is 7 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 665, 1008 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 665, 1008 is 7.
HCF(665, 1008) = 7
HCF of 665, 1008 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 1008 is 7.
Highest Common Factor of 665,1008 is 7
Step 1: Since 1008 > 665, we apply the division lemma to 1008 and 665, to get
1008 = 665 x 1 + 343
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 343 and 665, to get
665 = 343 x 1 + 322
Step 3: We consider the new divisor 343 and the new remainder 322, and apply the division lemma to get
343 = 322 x 1 + 21
We consider the new divisor 322 and the new remainder 21,and apply the division lemma to get
322 = 21 x 15 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 665 and 1008 is 7
Notice that 7 = HCF(21,7) = HCF(322,21) = HCF(343,322) = HCF(665,343) = HCF(1008,665) .
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Frequently Asked Questions on HCF of 665, 1008 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 665, 1008?
Answer: HCF of 665, 1008 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 1008 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 1008 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.