Highest Common Factor of 594, 495, 105 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 594, 495, 105 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 594, 495, 105 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 594, 495, 105 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 594, 495, 105 is 3.
HCF(594, 495, 105) = 3
HCF of 594, 495, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 594, 495, 105 is 3.
Highest Common Factor of 594,495,105 is 3
Step 1: Since 594 > 495, we apply the division lemma to 594 and 495, to get
594 = 495 x 1 + 99
Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 99 and 495, to get
495 = 99 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 99, the HCF of 594 and 495 is 99
Notice that 99 = HCF(495,99) = HCF(594,495) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 99, we apply the division lemma to 105 and 99, to get
105 = 99 x 1 + 6
Step 2: Since the reminder 99 ≠ 0, we apply division lemma to 6 and 99, to get
99 = 6 x 16 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 99 and 105 is 3
Notice that 3 = HCF(6,3) = HCF(99,6) = HCF(105,99) .
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Frequently Asked Questions on HCF of 594, 495, 105 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 594, 495, 105?
Answer: HCF of 594, 495, 105 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 594, 495, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 594, 495, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
