Highest Common Factor of 675, 456, 66 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, 456, 66 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 456, 66 is 3 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, 456, 66 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, 456, 66 is 3.
HCF(675, 456, 66) = 3
HCF of 675, 456, 66 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, 456, 66 is 3.
Highest Common Factor of 675,456,66 is 3
Step 1: Since 675 > 456, we apply the division lemma to 675 and 456, to get
675 = 456 x 1 + 219
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 219 and 456, to get
456 = 219 x 2 + 18
Step 3: We consider the new divisor 219 and the new remainder 18, and apply the division lemma to get
219 = 18 x 12 + 3
We consider the new divisor 18 and the new remainder 3, and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 675 and 456 is 3
Notice that 3 = HCF(18,3) = HCF(219,18) = HCF(456,219) = HCF(675,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 3, we apply the division lemma to 66 and 3, to get
66 = 3 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 66 is 3
Notice that 3 = HCF(66,3) .
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Frequently Asked Questions on HCF of 675, 456, 66 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, 456, 66?
Answer: HCF of 675, 456, 66 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 456, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 456, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
