Highest Common Factor of 456, 684, 852 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 456, 684, 852 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 456, 684, 852 is 12 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 456, 684, 852 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 456, 684, 852 is 12.
HCF(456, 684, 852) = 12
HCF of 456, 684, 852 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 456, 684, 852 is 12.
Highest Common Factor of 456,684,852 is 12
Step 1: Since 684 > 456, we apply the division lemma to 684 and 456, to get
684 = 456 x 1 + 228
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 228 and 456, to get
456 = 228 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 228, the HCF of 456 and 684 is 228
Notice that 228 = HCF(456,228) = HCF(684,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 852 > 228, we apply the division lemma to 852 and 228, to get
852 = 228 x 3 + 168
Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 168 and 228, to get
228 = 168 x 1 + 60
Step 3: We consider the new divisor 168 and the new remainder 60, and apply the division lemma to get
168 = 60 x 2 + 48
We consider the new divisor 60 and the new remainder 48,and apply the division lemma to get
60 = 48 x 1 + 12
We consider the new divisor 48 and the new remainder 12,and apply the division lemma to get
48 = 12 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 228 and 852 is 12
Notice that 12 = HCF(48,12) = HCF(60,48) = HCF(168,60) = HCF(228,168) = HCF(852,228) .
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Frequently Asked Questions on HCF of 456, 684, 852 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 456, 684, 852?
Answer: HCF of 456, 684, 852 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 456, 684, 852 using Euclid's Algorithm?
Answer: For arbitrary numbers 456, 684, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.