Highest Common Factor of 675, 990 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 675, 990 i.e. 45 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 990 is 45 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 675, 990 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 675, 990 is 45.
HCF(675, 990) = 45
HCF of 675, 990 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 990 is 45.
Highest Common Factor of 675,990 is 45
Step 1: Since 990 > 675, we apply the division lemma to 990 and 675, to get
990 = 675 x 1 + 315
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 315 and 675, to get
675 = 315 x 2 + 45
Step 3: We consider the new divisor 315 and the new remainder 45, and apply the division lemma to get
315 = 45 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 675 and 990 is 45
Notice that 45 = HCF(315,45) = HCF(675,315) = HCF(990,675) .
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Frequently Asked Questions on HCF of 675, 990 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 675, 990?
Answer: HCF of 675, 990 is 45 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 990 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
