Highest Common Factor of 756, 288, 154 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 756, 288, 154 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 756, 288, 154 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 756, 288, 154 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 756, 288, 154 is 2.
HCF(756, 288, 154) = 2
HCF of 756, 288, 154 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 756, 288, 154 is 2.
Highest Common Factor of 756,288,154 is 2
Step 1: Since 756 > 288, we apply the division lemma to 756 and 288, to get
756 = 288 x 2 + 180
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 180 and 288, to get
288 = 180 x 1 + 108
Step 3: We consider the new divisor 180 and the new remainder 108, and apply the division lemma to get
180 = 108 x 1 + 72
We consider the new divisor 108 and the new remainder 72,and apply the division lemma to get
108 = 72 x 1 + 36
We consider the new divisor 72 and the new remainder 36,and apply the division lemma to get
72 = 36 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 756 and 288 is 36
Notice that 36 = HCF(72,36) = HCF(108,72) = HCF(180,108) = HCF(288,180) = HCF(756,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 154 > 36, we apply the division lemma to 154 and 36, to get
154 = 36 x 4 + 10
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 10 and 36, to get
36 = 10 x 3 + 6
Step 3: We consider the new divisor 10 and the new remainder 6, and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 36 and 154 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(36,10) = HCF(154,36) .
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Frequently Asked Questions on HCF of 756, 288, 154 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 756, 288, 154?
Answer: HCF of 756, 288, 154 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 756, 288, 154 using Euclid's Algorithm?
Answer: For arbitrary numbers 756, 288, 154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
