Highest Common Factor of 852, 1442 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 852, 1442 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 852, 1442 is 2 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 852, 1442 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 852, 1442 is 2.
HCF(852, 1442) = 2
HCF of 852, 1442 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 852, 1442 is 2.
Highest Common Factor of 852,1442 is 2
Step 1: Since 1442 > 852, we apply the division lemma to 1442 and 852, to get
1442 = 852 x 1 + 590
Step 2: Since the reminder 852 ≠ 0, we apply division lemma to 590 and 852, to get
852 = 590 x 1 + 262
Step 3: We consider the new divisor 590 and the new remainder 262, and apply the division lemma to get
590 = 262 x 2 + 66
We consider the new divisor 262 and the new remainder 66,and apply the division lemma to get
262 = 66 x 3 + 64
We consider the new divisor 66 and the new remainder 64,and apply the division lemma to get
66 = 64 x 1 + 2
We consider the new divisor 64 and the new remainder 2,and apply the division lemma to get
64 = 2 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 852 and 1442 is 2
Notice that 2 = HCF(64,2) = HCF(66,64) = HCF(262,66) = HCF(590,262) = HCF(852,590) = HCF(1442,852) .
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Frequently Asked Questions on HCF of 852, 1442 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 852, 1442?
Answer: HCF of 852, 1442 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 852, 1442 using Euclid's Algorithm?
Answer: For arbitrary numbers 852, 1442 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.