Highest Common Factor of 828, 360, 53 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 828, 360, 53 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 828, 360, 53 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 828, 360, 53 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 828, 360, 53 is 1.
HCF(828, 360, 53) = 1
HCF of 828, 360, 53 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 828, 360, 53 is 1.
Highest Common Factor of 828,360,53 is 1
Step 1: Since 828 > 360, we apply the division lemma to 828 and 360, to get
828 = 360 x 2 + 108
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 108 and 360, to get
360 = 108 x 3 + 36
Step 3: We consider the new divisor 108 and the new remainder 36, and apply the division lemma to get
108 = 36 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 828 and 360 is 36
Notice that 36 = HCF(108,36) = HCF(360,108) = HCF(828,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 53 > 36, we apply the division lemma to 53 and 36, to get
53 = 36 x 1 + 17
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 17 and 36, to get
36 = 17 x 2 + 2
Step 3: We consider the new divisor 17 and the new remainder 2, and apply the division lemma to get
17 = 2 x 8 + 1
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 36 and 53 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(36,17) = HCF(53,36) .
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Frequently Asked Questions on HCF of 828, 360, 53 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 828, 360, 53?
Answer: HCF of 828, 360, 53 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 828, 360, 53 using Euclid's Algorithm?
Answer: For arbitrary numbers 828, 360, 53 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.