Highest Common Factor of 168, 560, 92 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 168, 560, 92 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 168, 560, 92 is 4 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 168, 560, 92 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 168, 560, 92 is 4.
HCF(168, 560, 92) = 4
HCF of 168, 560, 92 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 168, 560, 92 is 4.
Highest Common Factor of 168,560,92 is 4
Step 1: Since 560 > 168, we apply the division lemma to 560 and 168, to get
560 = 168 x 3 + 56
Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 56 and 168, to get
168 = 56 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 56, the HCF of 168 and 560 is 56
Notice that 56 = HCF(168,56) = HCF(560,168) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 92 > 56, we apply the division lemma to 92 and 56, to get
92 = 56 x 1 + 36
Step 2: Since the reminder 56 ≠ 0, we apply division lemma to 36 and 56, to get
56 = 36 x 1 + 20
Step 3: We consider the new divisor 36 and the new remainder 20, and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 56 and 92 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(56,36) = HCF(92,56) .
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Frequently Asked Questions on HCF of 168, 560, 92 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 168, 560, 92?
Answer: HCF of 168, 560, 92 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 168, 560, 92 using Euclid's Algorithm?
Answer: For arbitrary numbers 168, 560, 92 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.