Highest Common Factor of 360, 904, 68 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 360, 904, 68 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 904, 68 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 360, 904, 68 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 360, 904, 68 is 4.
HCF(360, 904, 68) = 4
HCF of 360, 904, 68 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 904, 68 is 4.
Highest Common Factor of 360,904,68 is 4
Step 1: Since 904 > 360, we apply the division lemma to 904 and 360, to get
904 = 360 x 2 + 184
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 184 and 360, to get
360 = 184 x 1 + 176
Step 3: We consider the new divisor 184 and the new remainder 176, and apply the division lemma to get
184 = 176 x 1 + 8
We consider the new divisor 176 and the new remainder 8, and apply the division lemma to get
176 = 8 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 360 and 904 is 8
Notice that 8 = HCF(176,8) = HCF(184,176) = HCF(360,184) = HCF(904,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 8, we apply the division lemma to 68 and 8, to get
68 = 8 x 8 + 4
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 4 and 8, to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8 and 68 is 4
Notice that 4 = HCF(8,4) = HCF(68,8) .
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Frequently Asked Questions on HCF of 360, 904, 68 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 360, 904, 68?
Answer: HCF of 360, 904, 68 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 904, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 904, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.