Highest Common Factor of 864, 504, 639, 468 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 864, 504, 639, 468 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 864, 504, 639, 468 is 9 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 864, 504, 639, 468 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 864, 504, 639, 468 is 9.
HCF(864, 504, 639, 468) = 9
HCF of 864, 504, 639, 468 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 864, 504, 639, 468 is 9.
Highest Common Factor of 864,504,639,468 is 9
Step 1: Since 864 > 504, we apply the division lemma to 864 and 504, to get
864 = 504 x 1 + 360
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 360 and 504, to get
504 = 360 x 1 + 144
Step 3: We consider the new divisor 360 and the new remainder 144, and apply the division lemma to get
360 = 144 x 2 + 72
We consider the new divisor 144 and the new remainder 72, and apply the division lemma to get
144 = 72 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 72, the HCF of 864 and 504 is 72
Notice that 72 = HCF(144,72) = HCF(360,144) = HCF(504,360) = HCF(864,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 639 > 72, we apply the division lemma to 639 and 72, to get
639 = 72 x 8 + 63
Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 63 and 72, to get
72 = 63 x 1 + 9
Step 3: We consider the new divisor 63 and the new remainder 9, and apply the division lemma to get
63 = 9 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 72 and 639 is 9
Notice that 9 = HCF(63,9) = HCF(72,63) = HCF(639,72) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 468 > 9, we apply the division lemma to 468 and 9, to get
468 = 9 x 52 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 468 is 9
Notice that 9 = HCF(468,9) .
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Frequently Asked Questions on HCF of 864, 504, 639, 468 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 864, 504, 639, 468?
Answer: HCF of 864, 504, 639, 468 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 864, 504, 639, 468 using Euclid's Algorithm?
Answer: For arbitrary numbers 864, 504, 639, 468 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
