Highest Common Factor of 489, 756, 504, 122 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 489, 756, 504, 122 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 489, 756, 504, 122 is 1 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 489, 756, 504, 122 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 489, 756, 504, 122 is 1.
HCF(489, 756, 504, 122) = 1
HCF of 489, 756, 504, 122 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 489, 756, 504, 122 is 1.
Highest Common Factor of 489,756,504,122 is 1
Step 1: Since 756 > 489, we apply the division lemma to 756 and 489, to get
756 = 489 x 1 + 267
Step 2: Since the reminder 489 ≠ 0, we apply division lemma to 267 and 489, to get
489 = 267 x 1 + 222
Step 3: We consider the new divisor 267 and the new remainder 222, and apply the division lemma to get
267 = 222 x 1 + 45
We consider the new divisor 222 and the new remainder 45,and apply the division lemma to get
222 = 45 x 4 + 42
We consider the new divisor 45 and the new remainder 42,and apply the division lemma to get
45 = 42 x 1 + 3
We consider the new divisor 42 and the new remainder 3,and apply the division lemma to get
42 = 3 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 489 and 756 is 3
Notice that 3 = HCF(42,3) = HCF(45,42) = HCF(222,45) = HCF(267,222) = HCF(489,267) = HCF(756,489) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 504 > 3, we apply the division lemma to 504 and 3, to get
504 = 3 x 168 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 504 is 3
Notice that 3 = HCF(504,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 122 > 3, we apply the division lemma to 122 and 3, to get
122 = 3 x 40 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 122 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(122,3) .
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Frequently Asked Questions on HCF of 489, 756, 504, 122 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 489, 756, 504, 122?
Answer: HCF of 489, 756, 504, 122 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 489, 756, 504, 122 using Euclid's Algorithm?
Answer: For arbitrary numbers 489, 756, 504, 122 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.